Equation Equilibrium Answer Key
EQUATIONS QUIZ
Answer Key
Step-by-Step Solutions & Scoring Guide (Questions 1–5)
Directions: Solve each equation.
Step-by-step worked solutions
1. Solution \(x - 14 = -29\)
Add 14 to both sides:
\(x = -29 + 14\)
\(x = -15\)
Correct Value: x = -15
2. Solution \(-\frac{3}{4}m = 18\)
Multiply by reciprocal \(-\frac{4}{3}\):
\(m = 18 \cdot \left(-\frac{4}{3}\right) = \frac{-72}{3}\)
\(m = -24\)
Correct Value: m = -24
3. Solution \(\frac{y}{-6} = 4.5\)
Multiply both sides by -6:
\(y = 4.5 \cdot (-6)\)
\(y = -27\)
Correct Value: y = -27
4. Solution \(5x - 17 = -42\)
Add 17: \(5x = -42 + 17 \implies 5x = -25\)
Divide by 5: \(\frac{5x}{5} = \frac{-25}{5}\)
\(x = -5\)
Correct Value: x = -5
5. Solution \(\frac{2}{3}w + 9 = 1\)
Subtract 9: \(\frac{2}{3}w = 1 - 9 \implies \frac{2}{3}w = -8\)
Multiply by reciprocal \(\frac{3}{2}\): \(w = -8 \cdot \frac{3}{2} = \frac{-24}{2}\)
\(w = -12\)
Correct Value: w = -12
Teacher Key • Page 1 of 2 Turn over for Solutions 6–10 →
EQUATIONS QUIZ | Teacher Answer Key (Questions 6–10)
Directions: Solve each equation.
6. Solution \(4(2a - 5) = 28\)
Distribute 4: \(8a - 20 = 28\)
Add 20: \(8a = 48\)
Divide by 8: \(a = 6\)
Correct Value: a = 6
7. Solution \(3(2x - 4) - 5x = 9\)
Distribute 3: \(6x - 12 - 5x = 9\)
Combine terms: \(x - 12 = 9\)
Add 12: \(x = 21\)
Correct Value: x = 21
8. Solution \(8y - 15 = 3y + 20\)
Subtract \(3y\): \(5y - 15 = 20\)
Add 15: \(5y = 35\)
Divide by 5: \(y = 7\)
Correct Value: y = 7
9. Solution \(4(3m + 2) = 7m - 12\)
Distribute 4: \(12m + 8 = 7m - 12\)
Subtract \(7m\): \(5m + 8 = -12\)
Subtract 8: \(5m = -20 \implies\) \(m = -4\)
Correct Value: m = -4
10. Solution \(4(2x - 1) = 3x + 16\)
Step 1 (Distribute): \(8x - 4 = 3x + 16\)
Step 2 (Subtract \(3x\)): \(5x - 4 = 16\)
Step 3 (Add 4 & Divide by 5): \(5x = 20 \implies\) \(x = 4\)
Check: LHS = \(4(2(4) - 1) = 4(7) = 28\); RHS = \(3(4) + 16 = 28\). Valid.
Correct Value: x = 4
Teacher Key • Page 2 of 2 End of Answer Key