smc-4215-27-Multi-step

Equations, SM-Bank 095

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

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\(x=6\)

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

Equations, SM-Bank 094

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

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\(n=2\)

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

Equations, SM-Bank 093

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

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\(y=3\)

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

Equations, SM-Bank 092

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

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\(m=-5\)

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

Equations, SM-Bank 091

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

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\(x=3\)

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

Equations, SM-Bank 090

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

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\(x=8\)

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

Equations, SM-Bank 089

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

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

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

Equations, SM-Bank 088

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

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

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

Equations, SM-Bank 087

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

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\(y=-6\)

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

Equations, SM-Bank 086

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

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\(x=-9\)

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

Equations, SM-Bank 085

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

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

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

Equations, SM-Bank 084

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

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\(t=5\)

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

Equations, SM-Bank 083

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

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

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

Equations, SM-Bank 082

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

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\(z=1\)

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

Equations, SM-Bank 081

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

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

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

Equations, SM-Bank 080

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

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

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

Equations, SM-Bank 079

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

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\(x=-2\)

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

Equations, SM-Bank 078

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

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\(a=3\)

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

Equations, SM-Bank 076

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

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\(b=6\)

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

Equations, SM-Bank 077

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

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\(x=2\)

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

Equations, SM-Bank 075

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

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\(m=3\)

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

Equations, SM-Bank 074

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

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\(p=-4\)

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

Equations, SM-Bank 073

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

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\(q=-14\)

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

Equations, SM-Bank 072

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

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\(y=-3\)

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

Equations, SM-Bank 071

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

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\(m=1\)

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

Equations, SM-Bank 070

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

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\(x=13\)

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