Solving Linear Equations: math test solutions, Grade 9 – download the PDF

1 Expressions and order of operations / 3 pts

1. \(9+14=23\). (1 pt)
2. \(5+3\cdot 5^2=5+75=80\). (1 pt)
3. \(2\cdot 9-12=6\). (1 pt)

2 One-step and two-step equations / 3 pts

1. \(x=21\). (1 pt)
2. \(y=-9\). (1 pt)
3. \(5k=-25\), so \(k=-5\). (1 pt)

3 Multi-step equations / 4 pts

1. \(8x-12+5=33\), so \(8x-7=33\), \(8x=40\) and \(x=5\). (2 pts)
2. \(7x-2x+8=23\), so \(5x=15\) and \(x=3\). (2 pts)

4 Variables on both sides / 4 pts

1. \(4x=16\), so \(x=4\). (2 pts)
2. \(3x+12=5x-2\), so \(14=2x\) and \(x=7\). (2 pts)

5 Ride-share fare / 3 pts

Equation: \(2m+3=21\). (1 pt)

Subtract 3: \(2m=18\). (1 pt)

The ride was \(m=9\) miles long. Check: \(2\cdot 9+3=21\). (1 pt)

6 Formulas and special cases / 3 pts

1. \(h=\dfrac{2A}{b}\). (1 pt)
2. \(h=\dfrac{60}{12}=5\). (1 pt)
3. Subtracting \(4x\) gives \(-1=3\), false: no solution. (1 pt)