Multi-Step Equations Unit Test

Answer 1

Sure! Here are some multi-step equation problems that you can use to test your understanding of this topic. Each question comes with a solution.

Multi-Step Equations Unit Test

Questions

1. Solve for \( x \): \[ 3(x - 4) + 2 = 11 \]

2. Solve for \( y \): \[ 5(2y + 3) - 4 = 3y + 18 \]

3. Solve for \( z \): \[ 4z - 7 = 3(2z + 1) - 1 \]

4. Solve for \( a \): \[ 7 - 2(3a - 5) = 9 \]

5. Solve for \( b \): \[ 6b + 4 - 3(b + 2) = 2b + 10 \]

Solutions

1. For \( x \): \[ 3(x - 4) + 2 = 11 \] \[ 3x - 12 + 2 = 11 \] \[ 3x - 10 = 11 \] \[ 3x = 21 \] \[ x = 7 \]

2. For \( y \): \[ 5(2y + 3) - 4 = 3y + 18 \] \[ 10y + 15 - 4 = 3y + 18 \] \[ 10y + 11 = 3y + 18 \] \[ 10y - 3y = 18 - 11 \] \[ 7y = 7 \] \[ y = 1 \]

3. For \( z \): \[ 4z - 7 = 3(2z + 1) - 1 \] \[ 4z - 7 = 6z + 3 - 1 \] \[ 4z - 7 = 6z + 2 \] \[ -7 - 2 = 6z - 4z \] \[ -9 = 2z \] \[ z = -\frac{9}{2} \quad \text{or} \quad z = -4.5 \]

4. For \( a \): \[ 7 - 2(3a - 5) = 9 \] \[ 7 - 6a + 10 = 9 \] \[ 17 - 6a = 9 \] \[ -6a = 9 - 17 \] \[ -6a = -8 \] \[ a = \frac{4}{3} \]

5. For \( b \): \[ 6b + 4 - 3(b + 2) = 2b + 10 \] \[ 6b + 4 - 3b - 6 = 2b + 10 \] \[ 3b - 2 = 2b + 10 \] \[ 3b - 2b = 10 + 2 \] \[ b = 12 \]

Scoring

You can grade yourself based on how many problems you got correct. Each correct answer could be worth a point, giving you a total score out of 5.

Good luck with your studies on multi-step equations! Let me know if you need more practice or further explanation on any problem!