smc-4215-20-Two-step

Equations, SM-Bank 055

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

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\(x=4.5\)

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

Equations, SM-Bank 054

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

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\(x=9\)

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

Equations, SM-Bank 048

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

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

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

Equations, SM-Bank 047

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

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\(x=15\)

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

Equations, SM-Bank 046

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

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\(x=-12\)

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

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

Equations, SM-Bank 036

Solve the equation \(\dfrac{2x}{3}=10\). (2 marks)

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\(x=15\)

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\(\dfrac{2x}{3}\)	\(=10\)
\(2x\)	\(=10\times 3\)
\(2x\)	\(=30\)
\(x\)	\(=15\)

Equations, SM-Bank 035

Two consecutive integers have a sum of 147.

Given the first number is \(x\), write an algebraic equation to represent this information. (2 marks)

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Solve your equation algebraically to find the two numbers. (2 marks)

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a. \(2x+1=147\)

b. \(73 , 74\)

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a. \(\text{Given the 1st number is}\ x\text{, the 2nd number is }x+1.\)

\(\therefore\ \text{Equation is:}\)

\(x+(x+1)\)	\(=147\)
\(2x+1\)	\(=147\)

b.	\(2x+1\)	\(=147\)
	\(2x\)	\(=146\)
	\(x\)	\(=73\)

\(\therefore\ \text{Numbers are }73\ \text{and }74.\)

Equations, SM-Bank 034

Two consecutive integers have a sum of 25.

Given the first number is \(x\), write an algebraic equation to represent this information. (2 marks)

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Solve your equation algebraically to find the two numbers. (2 marks)

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a. \(2x+1=25\)

a. \(12 , 13\)

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a. \(\text{Given the 1st number is}\ x\text{, the 2nd number is }x+1.\)

\(\therefore\ \text{Equation is:}\)

\(x+(x+1)\)	\(=25\)
\(2x+1\)	\(=25\)

b.	\(2x+1\)	\(=25\)
	\(2x\)	\(=24\)
	\(x\)	\(=12\)

\(\therefore\ \text{Numbers are }12\ \text{and }13.\)

Equations, SM-Bank 027

Solve \(2x+3=4x\). (2 marks)

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

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

Equations, SM-Bank 026

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

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\(x=2\)

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\(\dfrac{x+4}{3}\)	\(=2\)
\(x+4\)	\(=2\times 3\)
\(x+4\)	\(=6\)
\(x\)	\(=6-4\)
\(x\)	\(=2\)

Equations, SM-Bank 025

\(3\) is subtracted from a quarter of \(x\) and the result is \(-\dfrac{1}{2}\).

Write an equation and solve it algebraically to find the value of \(x\). (3 marks)

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\(x=10\)

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\(\dfrac{x}{4}-3\)	\(=-\dfrac{1}{2}\)
\(\dfrac{x}{4}\)	\(=-\dfrac{1}{2}+3\)
\(\dfrac{x}{4}\)	\(=2\dfrac{1}{2}\)
\(x\)	\(=4\times 2\dfrac{1}{2}\)
\(x\)	\(=10\)

Equations, SM-Bank 024

Solve \(4c-5.4=-7\) (2 marks)

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\(c=-0.4\)

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\(4c-5.4\)	\(=-7\)
\(4c\)	\(=-7+5.4\)
\(4c\)	\(=-1.6\)
\(c\)	\(=\dfrac{-1.6}{4}\)
\(c\)	\(=-0.4\)

Equations, SM-Bank 023

Solve \(10b-3=-2\) (2 marks)

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\(b=0.1\)

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\(10b-3\)	\(=-2\)
\(10b\)	\(=-2+3\)
\(10b\)	\(=1\)
\(b\)	\(=\dfrac{1}{10}\)
\(b\)	\(=0.1\)

Equations, SM-Bank 022

Solve \(\dfrac{q-4}{2}=6\) (2 marks)

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\(q=16\)

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\(\dfrac{q-4}{2}\)	\(=6\)
\(q-4\)	\(=6\times 2\)
\(q-4\)	\(=12\)
\(q\)	\(=12+4\)
\(q\)	\(=16\)

Equations, SM-Bank 021

Solve \(\dfrac{x+1}{3}=-4\) (2 marks)

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\(x=-13\)

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\(\dfrac{x+1}{3}\)	\(=-4\)
\(x+1\)	\(=-4\times 3\)
\(x+1\)	\(=-12\)
\(x\)	\(=-12-1\)
\(x\)	\(=-13\)

Equations, SM-Bank 020

Solve \(8-\dfrac{x}{9}=-1\) (2 marks)

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\(x=81\)

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\(8-\dfrac{x}{9}\)	\(=-1\)
\(\dfrac{-x}{9}\)	\(=-1-8\)
\(\dfrac{-x}{9}\)	\(=-9\)
\(-x\)	\(=-9\times 9\)
\(-x\)	\(=-81\)
\(x\)	\(=81\)

Equations, SM-Bank 019

Solve \(\dfrac{g}{4}+2=7\) (2 marks)

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\(g=20\)

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\(\dfrac{g}{4}+2\)	\(=7\)
\(\dfrac{g}{4}\)	\(=7-2\)
\(\dfrac{g}{4}\)	\(=5\)
\(g\)	\(=5\times 4\)
\(g\)	\(=20\)

Equation, SM-Bank 018

Solve \(10-7y=-11\) (2 marks)

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\(y=3\)

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\(10-7y\)	\(=-11\)
\(-7y\)	\(=-11-10\)
\(-7y\)	\(=-21\)
\(y\)	\(=\dfrac{-21}{-7}\)
\(y\)	\(=3\)

Equations, SM-Bank 017

Solve \(3m-8=-26\) (2 marks)

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\(m=-6\)

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\(3m-8\)	\(=-26\)
\(3m\)	\(=-26+8\)
\(3m\)	\(=-18\)
\(m\)	\(=\dfrac{-18}{3}\)
\(m\)	\(=-6\)

Equations, SM-Bank 016

Solve \(2x+3=9\) (2 marks)

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\(x=3\)

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\(2x+3\)	\(=9\)
\(2x\)	\(=9-3\)
\(2x\)	\(=6\)
\(x\)	\(=\dfrac{6}{2}\)
\(x\)	\(=3\)