Equations

Equations, SM-Bank 095

Solve \(2x-5=\dfrac{x}{2}+4\) (3 marks)

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\(x=6\)

Show Worked Solution

\(2x-5\)	\(=\dfrac{x}{2}+4\)
\(2\times (2x-5)\)	\(=2\times\left(\dfrac{x}{2}+4\right)\)
\(4x-10\)	\(=x+8\)
\(4x-x\)	\(=8+10\)
\(3x\)	\(=18\)
\(x\)	\(=6\)

Equations, SM-Bank 094

Solve \(4n=3+\dfrac{5n}{2}\) (3 marks)

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\(n=2\)

Show Worked Solution

\(4n\)	\(=3+\dfrac{5n}{2}\)
\(2\times 4n\)	\(=2\times\left(3+\dfrac{5n}{2}\right)\)
\(8n\)	\(=6+5n\)
\(8n-5n\)	\(=6\)
\(3n\)	\(=6\)
\(n\)	\(=2\)

Equations, SM-Bank 093

Solve \(3y=7+\dfrac{2y}{3}\) (3 marks)

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\(y=3\)

Show Worked Solution

\(3y\)	\(=7+\dfrac{2y}{3}\)
\(3\times 3y\)	\(=3\times\left(7+\dfrac{2y}{3}\right)\)
\(9y\)	\(=21+2y\)
\(9y-2y\)	\(=21\)
\(7y\)	\(=21\)
\(y\)	\(=3\)

Equations, SM-Bank 092

Solve \(\dfrac{4m}{5}-6=2m\) (3 marks)

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\(m=-5\)

Show Worked Solution

\(\dfrac{4m}{5}-6\)	\(=2m\)
\(5\times\left(\dfrac{4m}{5}-6\right)\)	\(=5\times 2m\)
\(4m-30\)	\(=10m\)
\(4m-10m\)	\(=30\)
\(-6m\)	\(=30\)
\(m\)	\(=-5\)

Equations, SM-Bank 091

Solve \(\dfrac{5x}{3}+1=2x\) (3 marks)

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\(x=3\)

Show Worked Solution

\(\dfrac{5x}{3}+1\)	\(=2x\)
\(3\times\left(\dfrac{5x}{3}+1\right)\)	\(=3\times 2x\)
\(5x+3\)	\(=6x\)
\(5x-6x\)	\(=-3\)
\(-x\)	\(=-3\)
\(x\)	\(=3\)

Equations, SM-Bank 090

Solve \(\dfrac{3x}{2}-4=x\) (3 marks)

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\(x=8\)

Show Worked Solution

\(\dfrac{3x}{2}-4\)	\(=x\)
\(2\times\left(\dfrac{3x}{2}-4\right)\)	\(=2\times x\)
\(3x-8\)	\(=2x\)
\(3x-2x\)	\(=8\)
\(x\)	\(=8\)

Equations, SM-Bank 089

Solve \(7-2w=3(4-5w)\) (3 marks)

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\(w=\dfrac{5}{13}\)

Show Worked Solution

\(7-2w\)	\(=3(4-5w)\)
\(7-2w\)	\(=12-15w\)
\(-2w+15w\)	\(=12-7\)
\(13w\)	\(=5\)
\(w\)	\(=\dfrac{5}{13}\)

Equations, SM-Bank 088

Solve \(4p-3=5(1-p)\) (3 marks)

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\(p=\dfrac{8}{9}\)

Show Worked Solution

\(4p-3\)	\(=5(1-p)\)
\(4p-3\)	\(=5-5p\)
\(4p+5p\)	\(=5+3\)
\(9p\)	\(=8\)
\(p\)	\(=\dfrac{8}{9}\)

Equations, SM-Bank 087

Solve \(3(y-2)=5y+6\) (3 marks)

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\(y=-6\)

Show Worked Solution

\(3(y-2)\)	\(=5y+6\)
\(3y-6\)	\(=5y+6\)
\(3y-5y\)	\(=6+6\)
\(-2y\)	\(=12\)
\(y\)	\(=\dfrac{12}{-2}=-6\)

Equations, SM-Bank 086

Solve \(2(x+1)=x-7\) (3 marks)

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\(x=-9\)

Show Worked Solution

\(2(x+1)\)	\(=x-7\)
\(2x+2\)	\(=x-7\)
\(2x-x\)	\(=-7-2\)
\(x\)	\(=-9\)

Equations, SM-Bank 085

Solve \(8x+3=5x-7\) (3 marks)

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\(x=-\dfrac{10}{3}\ \text{or }-3\dfrac{1}{3}\)

Show Worked Solution

\(8x+3\)	\(=5x-7\)
\(8x-5x\)	\(=-7-3\)
\(3x\)	\(=-10\)
\(x\)	\(=-\dfrac{10}{3}=-3\dfrac{1}{3}\)

Equations, SM-Bank 084

Solve \(2t+13=7t-12\) (3 marks)

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\(t=5\)

Show Worked Solution

\(2t+13\)	\(=7t-12\)
\(2t-7t\)	\(=-12-13\)
\(-5t\)	\(=-25\)
\(t\)	\(=\dfrac{-25}{-5}=5\)

Equations, SM-Bank 083

Solve \(5-4m=-1+m\) (3 marks)

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\(m=\dfrac{6}{5}\)

Show Worked Solution

\(5-4m\)	\(=-1+m\)
\(-4m-m\)	\(=-1-5\)
\(-5m\)	\(=-6\)
\(m\)	\(=\dfrac{-6}{-5}=\dfrac{6}{5}\)

Equations, SM-Bank 082

Solve \(11z-2=5z+4\) (2 marks)a

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\(z=1\)

Show Worked Solution

\(11z-2\)	\(=5z+4\)
\(11z-5z\)	\(=4+2\)
\(6z\)	\(=6\)
\(z\)	\(=1\)

Equations, SM-Bank 081

Solve \(7w+6=8-3w\) (3 marks)

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\(w=\dfrac{1}{5}\)

Show Worked Solution

\(7w+6\)	\(=8-3w\)
\(7w+3w\)	\(=8-6\)
\(10w\)	\(=2\)
\(w\)	\(=\dfrac{2}{10}=\dfrac{1}{5}\)

Equations, SM-Bank 080

Solve \(7q-5=-3q-10\) (2 marks)

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\(q=-\dfrac{1}{2}\)

Show Worked Solution

\(7q-5\)	\(=-3q-10\)
\(7q+3q\)	\(=-10+5\)
\(10q\)	\(=-5\)
\(q\)	\(=-\dfrac{5}{10}=-\dfrac{1}{2}\)

Equations, SM-Bank 079

Solve \(5x-7=3x-11\) (2 marks)

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\(x=-2\)

Show Worked Solution

\(5x-7\)	\(=3x-11\)
\(5x-3x\)	\(=-11+7\)
\(2x\)	\(=-4\)
\(x\)	\(=-2\)

Equations, SM-Bank 078

Solve \(2a-1=8-a\) (2 marks)

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\(a=3\)

Show Worked Solution

\(2a-1\)	\(=8-a\)
\(2a+a\)	\(=8+1\)
\(3a\)	\(=9\)
\(a\)	\(=3\)

Equations, SM-Bank 076

Solve \(3b=30-2b\) (2 marks)

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\(b=6\)

Show Worked Solution

\(3b\)	\(=30-2b\)
\(3b+2b\)	\(=30\)
\(5b\)	\(=30\)
\(b\)	\(=6\)

Equations, SM-Bank 077

Solve \(4x=18-5x\) (2 marks)

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\(x=2\)

Show Worked Solution

\(4x\)	\(=18-5x\)
\(4x+5x\)	\(=18\)
\(9x\)	\(=18\)
\(x\)	\(=2\)

Equations, SM-Bank 075

Solve \(18m=9+15m\) (2 marks)

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\(m=3\)

Show Worked Solution

\(18m\)	\(=9+15m\)
\(18m-15m\)	\(=9\)
\(3m\)	\(=9\)
\(m\)	\(=3\)

Equations, SM-Bank 074

Solve \(8p-5=7p-9\) (2 marks)

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\(p=-4\)

Show Worked Solution

\(8p-5\)	\(=7p-9\)
\(8p-7p\)	\(=-9+5\)
\(p\)	\(=-4\)

Equations, SM-Bank 073

Solve \(2q+11=q-3\) (2 marks)

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\(q=-14\)

Show Worked Solution

\(2q+11\)	\(=q-3\)
\(2q-q\)	\(=-3-11\)
\(q\)	\(=-14\)

Equations, SM-Bank 072

Solve \(8y-1=7y-4\) (2 marks)

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\(y=-3\)

Show Worked Solution

\(8y-1\)	\(=7y-4\)
\(8y-7y\)	\(=-4+1\)
\(y\)	\(=-3\)

Equations, SM-Bank 071

Solve \(5m+4=2m+7\) (2 marks)

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\(m=1\)

Show Worked Solution

\(5m+4\)	\(=2m+7\)
\(5m-2m\)	\(=7-4\)
\(3m\)	\(=3\)
\(m\)	\(=1\)

Equations, SM-Bank 070

Solve \(3x-8=2x+5\) (2 marks)

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\(x=13\)

Show Worked Solution

\(3x-8\)	\(=2x+5\)
\(3x-2x\)	\(=5+8\)
\(x\)	\(=13\)

Equations, SM-Bank 069

Find the value of \(\large c\) in the formula \(c^2=a^2+b^2\) given \(a=12\) and \(b=14\). Assume \(\large c\) is positive and give your answer correct to 2 decimal places. (2 marks)

--- 5 WORK AREA LINES (style=lined) ---

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\(c\approx 18.44\)

Show Worked Solution

\(c^2\)	\(=a^2+b^2\)
\(c^2\)	\(=12^2+14^2\)
\(c^2\)	\(=144+196\)
\(\sqrt{c^2}\)	\(=\sqrt{340}\)
\(c\)	\(=18.4390\ldots\)
	\(\approx 18.44\)

Equations, SM-Bank 068

Find the value of \(\large c\) in the formula \(c^2=a^2+b^2\), given \(a=7\) and \(b=24\). Assume \(\large c\) is positive. (2 marks)

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\(c=25\)

Show Worked Solution

\(c^2\)	\(=a^2+b^2\)
\(c^2\)	\(=7^2+24^2\)
\(c^2\)	\(=49+576\)
\(\sqrt{c^2}\)	\(=\sqrt{625}\)
\(c\)	\(=25\)

Equations, SM-Bank 067

Find the value of \(\large r\) in the formula \(A=\pi r^2\) given \(A=10\). Assume \(\large r\) is positive and give your answer correct to 1 decimal place. (2 marks)

--- 5 WORK AREA LINES (style=lined) ---

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\(r\approx 1.8\)

Show Worked Solution

\(A\)	\(=\pi r^2\)
\(\pi r^2\)	\(=10\)
\(r^2\)	\(=\dfrac{10}{\pi}\)
\(\sqrt{r^2}\)	\(=\sqrt{\dfrac{10}{\pi}}\)
\(r\)	\(=1.784\ldots\)
	\(\approx 1.8\ (1\text{ d.p.})\)

Equations, SM-Bank 066

Solve the quadratic equation \(x^2+3=147\) for \(x<0\). (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

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\(x=-12\)

Show Worked Solution

\(x^2+3\)	\(=147\)
\(x^2\)	\(=147-3\)
\(x^2\)	\(=144\)
\(\sqrt{x^2}\)	\(=\sqrt{144}\)
\(x\)	\(=\pm12\)

\(\therefore\ \text{Since}\ x<0\ x=-12\)

Equations, SM-Bank 065

Solve the quadratic equation \(x^2-1=48\) for \(x>0\). (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

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\(x=7\)

Show Worked Solution

\(x^2-1\)	\(=48\)
\(x^2\)	\(=48+1\)
\(x^2\)	\(=49\)
\(\sqrt{x^2}\)	\(=\sqrt{49}\)
\(x\)	\(=\pm7\)

\(\therefore\ \text{Since}\ x>0\ \ x=7\)

Equations, SM-Bank 064

A square has an area of \(121\ \text{cm}^2\).

Find the side length of the square. (2 marks)

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Find the perimeter of the square. (2 marks)

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a. \(11\ \text{cm}\)

b. \(44\ \text{cm}\)

Show Worked Solution

a.	\(A\)	\(=s^2\)
	\(A\)	\(=121\ \ \text{(given)}\)
	\(\therefore\ s^2\)	\(=121\)
	\(\sqrt{s^2}\)	\(=\sqrt{121}\)
	\(s\)	\(=11\)

\(\text{Side length}=11\ \text{cm}\)

b.	\(\text{Perimeter}\)	\(=4\times s\)
		\(=4\times 11\)
		\(=44\)

\(\text{Perimeter}=44\ \text{cm}\)

Equations, SM-Bank 063

A square has an area of \(36\ \text{m}^2\).

Find the side length of the square. (2 marks)

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Find the perimeter of the square. (2 marks)

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a. \(6\ \text{m}\)

b. \(24\ \text{m}\)

Show Worked Solution

a.	\(A\)	\(=s^2\)
	\(A\)	\(=36\ \ \text{(given)}\)
	\(\therefore\ s^2\)	\(=36\)
	\(\sqrt{s^2}\)	\(=\sqrt{36}\)
	\(s\)	\(=6\)

\(\text{Side length}=6\ \text{m}\)

b.	\(\text{Perimeter}\)	\(=4\times s\)
		\(=4\times 6\)
		\(=24\)

\(\text{Perimeter}=24\ \text{m}\)

Equations, SM-Bank 062

Solve, giving all solutions correct to 1 decimal place.

\(x^2=8\) (2 marks)

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\(x^2=323\) (2 marks)

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a. \(x=\pm 2.8\)

b. \(x=\pm 18.0\)

Show Worked Solution

a.	\(x^2\)	\(=8\)
	\(\sqrt{x^2}\)	\(=\pm\sqrt{8}\)
	\(x\)	\(=\pm 2.828…\ =\pm 2.8\)

b.	\(x^2\)	\(=323\)
	\(\sqrt{x^2}\)	\(=\pm\sqrt{323}\)
	\(x\)	\(=\pm 17.972…\ =\pm 18.0\)

Equations, SM-Bank 061

Solve, giving all solutions.

\(x^2=25\) (2 marks)

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\(x^2=289\) (2 marks)

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a. \(x=\pm 5\)

b. \(x=\pm 17\)

Show Worked Solution

a.	\(x^2\)	\(=25\)
	\(\sqrt{x^2}\)	\(=\pm\sqrt{25}\)
	\(x\)	\(=\pm 5\)

b.	\(x^2\)	\(=289\)
	\(\sqrt{x^2}\)	\(=\pm\sqrt{289}\)
	\(x\)	\(=\pm 17\)

Equations, SM-Bank 060

Show that \(x^2=64\) has 2 solutions. (2 marks)

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\(\text{See worked solutions}\)

Show Worked Solution

\(8^2=8\times 8=64\ \ \therefore \ x=8\ \text{is a solution.}\)

\((-8)^2=-8\times -8=64\ \ \therefore \ x=-8\ \text{is a solution.}\)

\(\therefore x=8\ \text{and }x=-8\ \text{are both solutions of }x^2=64\)

Equations, SM-Bank 059

Show that \(x^2=100\) has 2 solutions. (2 marks)

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\(\text{See worked solutions}\)

Show Worked Solution

\(10^2=10\times 10=100\ \ \therefore \ x=10\ \text{is a solution.}\)

\((-10)^2=-10\times -10=100\ \ \therefore \ x=-10\ \text{is a solution.}\)

\(\therefore x=10\ \text{and }x=-10\ \text{are both solutions of }x^2=100\)

Equations, SM-Bank 058

Show that \(x^2=9\) has 2 solutions. (2 marks)

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\(\text{See worked solutions}\)

Show Worked Solution

\(3^2=3\times 3=9\ \ \therefore \ x=3\ \text{is a solution.}\)

\((-3)^2=-3\times -3=9\ \ \therefore \ x=-3\ \text{is a solution.}\)

\(\therefore x=3\ \text{and }x=-3\ \text{are both solutions of }x^2=9\)

Equations, SM-Bank 057 MC

Which of the following is not equal to \(16\)?

\(8^2\)
\((-4)^2\)
\(4\times 4\)
\(2^4\)

Show Answers Only

\(A\)

Show Worked Solution

\(\text{Option A: }\ \ \)	\(8^2=8\times 8=64\ne 16\)
\(\text{Option B: }\ \ \)	\((-4)^2=-4\times -4=16\ \ \checkmark\)
\(\text{Option C: }\ \ \)	\(4\times 4=16\ \ \checkmark\)
\(\text{Option D: }\ \ \)	\(2^4=2\times 2\times 2\times 2=16\ \ \checkmark\)

\(\Rightarrow A\)

Equations, SM-Bank 056 MC

Which of the following is not equal to \(9\)?

\(-3\times -3\)
\(4.5^2\)
\(\sqrt{81}\)
\(3^2\)

Show Answers Only

\(B\)

Show Worked Solution

\(\text{Option A: }\ \ \)	\(-3\times -3=9\ \ \checkmark\)
\(\text{Option B: }\ \ \)	\(4.5^2=20.25\ne 9\)
\(\text{Option C: }\ \ \)	\(\sqrt{81}=9\ \ \checkmark\)
\(\text{Option D: }\ \ \)	\(3^2=9\ \ \checkmark\)

\(\Rightarrow B\)

Equations, SM-Bank 056

The formula for converting degrees Celsius to Fahrenheit is \(F=\dfrac{9C}{5}+32\).

Find \(F\) is \(C=35\). (2 marks)

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Find \(C\) is \(F=68\). (2 marks)

--- 5 WORK AREA LINES (style=lined) ---

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a. \(F=95\)

b. \(C=20\)

Show Worked Solution

a.	\(F\)	\(=\dfrac{9C}{5}+32\)
	\(F\)	\(=\dfrac{9\times 35}{5}+32\)
	\(F\)	\(=\dfrac{315}{5}+32\)
	\(F\)	\(=63+32=95\)

b.	\(F\)	\(=\dfrac{9C}{5}+32\)
	\(68\)	\(=\dfrac{9C}{5}+32\)
	\(\dfrac{9C}{5}\)	\(=68-32\)
	\(\dfrac{9C}{5}\)	\(=36\)
	\(9C\)	\(=36\times 5\)
	\(9C\)	\(=180\)
	\(C\)	\(=\dfrac{180}{9}=20\)

Equations, SM-Bank 055

Solve \(2(x+3)=15\). (2 marks)

--- 5 WORK AREA LINES (style=lined) ---

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\(x=4.5\)

Show Worked Solution

\(2(x+3)\)	\(=15\)
\(2\times x+2\times 3\)	\(=15\)
\(2x+6\)	\(=15\)
\(2x\)	\(=9\)
\(x\)	\(=\dfrac{9}{2}\)
\(x\)	\(=4.5\)

Equations, SM-Bank 054

Solve \(3(x-1)=24\). (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

Show Answers Only

\(x=9\)

Show Worked Solution

\(3(x-1)\)	\(=24\)
\(3\times x+3\times -1\)	\(=24\)
\(3x-3\)	\(=24\)
\(3x\)	\(=27\)
\(x\)	\(=\dfrac{27}{3}\)
\(x\)	\(=9\)

Equations, SM-Bank 053

Write an algebraic equation for the perimeter of the rectangle below and use it to calculate the value of \(x\) given the perimeter is \(62\). (2 marks)

--- 5 WORK AREA LINES (style=lined) ---

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\(x=3\)

Show Worked Solution

\(P=2l+2w\)

\(62\)	\(=2(7x+1)+2\times 3x\)
\(62\)	\(=2\times 7x+2\times 1 +6x\)
\(62\)	\(=14x+2 +6x\)
\(20x+2\)	\(=62\)
\(20x\)	\(=60\)
\(x\)	\(=3\)

Equations, SM-Bank 052

An isosceles triangle has a perimeter of \(46\) and its base is 12. Find the length of its equal sides. (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

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\(l=17\)

Show Worked Solution

\(P\)	\(=2l+b\)
\(46\)	\(=2l+12\)
\(2l\)	\(=34\)
\(l\)	\(=\dfrac{34}{2}\)
\(l\)	\(=17\)

Equations, SM-Bank 051

A rectangle has a length of \(12\) and its area is 96. Find its width. (2 marks)

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\(w=8\)

Show Worked Solution

\(A\)	\(=l\times w\)
\(96\)	\(=12\times w\)
\(12w\)	\(=96\)
\(w\)	\(=\dfrac{96}{12}\)
\(w\)	\(=8\)

Equations, SM-Bank 050

Find the value of \(c\) in the formula \(c=\sqrt{a^2+b^2}\) if \(a=12\) and \(b=5\). (2 marks)

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\(c=13\)

Show Worked Solution

\(c\)	\(=\sqrt{a^2+b^2}\)
\(c\)	\(=\sqrt{12^2+5^2}\)
\(c\)	\(=\sqrt{144+25}\)
\(c\)	\(=\sqrt{169}\)
\(c\)	\(=13\)

Equations, SM-Bank 049

Find the value of \(a\) in the formula \(y=ax^2\) if \(y=32\) and \(x=4\). (2 marks)

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\(a=2\)

Show Worked Solution

\(y\)	\(=ax^2\)
\(32\)	\(=a\times 4^2 \)
\(16a\)	\(=32\)
\(a\)	\(=2\)

Equations, SM-Bank 048

Solve \(\dfrac{2n+3}{2}=-1\). (2 marks)

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\(n=-2\dfrac{1}{2}\)

Show Worked Solution

\(\dfrac{2n+3}{2}\)	\(=-1\)
\(2n+3\)	\(=-1\times 2\)
\(2n+3\)	\(=-2\)
\(2n\)	\(=-5\)
\(n\)	\(=\dfrac{-5}{2}\)
\(n\)	\(=-2\dfrac{1}{2}\)

Equations, SM-Bank 047

Solve \(\dfrac{3x}{5}-8=1\). (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

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\(x=15\)

Show Worked Solution

\(\dfrac{3x}{5}-8\)	\(=1\)
\(\dfrac{3x}{5}\)	\(=1+8\)
\(\dfrac{3x}{5}\)	\(=9\)
\(3x\)	\(=9\times 5\)
\(3x\)	\(=45\)
\(x\)	\(=15\)

Equations, SM-Bank 046

Solve \(\dfrac{2x}{3}=-8\). (2 marks)

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\(x=-12\)

Show Worked Solution

\(\dfrac{2x}{3}\)	\(=-8\)
\(2x\)	\(=-8\times 3\)
\(2x\)	\(=-24\)
\(x\)	\(=-12\)

Equations, SM-Bank 045

Find the value of \(L\) in the formula \(P=2L+2W\) if \(P=42\) and \(W=3\). (2 marks)

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\(L=18\)

Show Worked Solution

\(P\)	\(=2L+2W\)
\(42\)	\(=2L+2\times 3\)
\(42\)	\(=2L+6\)
\(2L\)	\(=36\)
\(L\)	\(=18\)

Equations, SM-Bank 044

Find the value of \(A\) in the formula \(A=\dfrac{h}{2}(a+b)\) if \(h=8\), \(a=7\) and \(b=3\). (2 marks)

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\(A=40\)

Show Worked Solution

\(A\)	\(=\dfrac{h}{2}(a+b)\)
\(A\)	\(=\dfrac{8}{2}(7+3)\)
\(A\)	\(=4\times 10\)
\(A\)	\(=40\)

Equations, SM-Bank 043

Find the value of \(y\) in the formula \(y=ax+b\) if \(a=4\), \(x=3\) and \(b=5\). (2 marks)

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\(y=17\)

Show Worked Solution

\(y\)	\(=ax+b\)
\(y\)	\(=4\times 3+5\)
\(y\)	\(=17\)

Equations, SM-Bank 042

Find the value of \(A\) in the formula \(A=\dfrac{1}{2}bh\) if \(b=32\) and \(h=10\). (2 marks)

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\(A=160\)

Show Worked Solution

\(A\)	\(=\dfrac{1}{2}bh\)
\(A\)	\(=\dfrac{1}{2}\times 32\times 10\)
\(A\)	\(=160\)

Equations, SM-Bank 040

Find the value of \(a\) in the formula \(2a+3b=c\) if \(b=2\) and \(c=10\). (2 marks)

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\(a=2\)

Show Worked Solution

\(2a+3b\)	\(=c\)
\(2a+3\times 2\)	\(=10\)
\(2a+6\)	\(=10\)
\(2a\)	\(=4\)
\(a\)	\(=2\)

Equations, SM-Bank 041

Find the value of \(h\) in the formula \(V=Ah\) if \(V=112\), and \(A=7\). (2 marks)

Show Answers Only

\(h=16\)

Show Worked Solution

\(V\)	\(=Ah\)
\(112\)	\(=7h\)
\(h\)	\(=\dfrac{112}{7}\)
\(h\)	\(=16\)

Equations, SM-Bank 039

Solve the equation \(\dfrac{2x}{7}=1\). (2 marks)

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\(x=3\dfrac{1}{2}\)

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\(\dfrac{2x}{7}\)	\(=1\)
\(2x\)	\(=1\times 7\)
\(2x\)	\(=7\)
\(x\)	\(=\dfrac{7}{2}=3\dfrac{1}{2}\)

Equations, SM-Bank 038

Solve the equation \(\dfrac{5x}{3}=1\). (2 marks)

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\(x=\dfrac{3}{5}\)

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\(\dfrac{5x}{3}\)	\(=1\)
\(5x\)	\(=1\times 3\)
\(5x\)	\(=3\)
\(x\)	\(=\dfrac{3}{5}\)

Equations, SM-Bank 37

Solve the equation \(\dfrac{3x}{4}=9\). (2 marks)

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\(x=12\)

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\(\dfrac{3x}{4}\)	\(=9\)
\(3x\)	\(=9\times 4\)
\(3x\)	\(=36\)
\(x\)	\(=12\)