Algebra 1 Solving Linear Equations in One Variable Test Solutions and Scoring (PDF)

a) Add 9: \(x = 23\).

b) Subtract 8: \(5x = -25\). Divide by 5: \(x = -5\).

Scoring: 1 point for each correct solution.

Subtract \(3x\): \(4x – 4 = 20\). Add 4: \(4x = 24\). Divide by 4.

\(x = 6\)

Scoring: 1 point for collecting variable terms and constants correctly; 1 point for the solution.

Distribute: \(8x – 12 = 3x + 13\). Subtract \(3x\): \(5x – 12 = 13\). Add 12: \(5x = 25\).

\(x = 5\)

Scoring: 1 point for distributing correctly; 1 point for the solution.

Subtract 2: \(\frac{3}{4}x = 9\). Multiply by \(\frac{4}{3}\): \(x = 9 \cdot \frac{4}{3} = 12\).

\(x = 12\)

Scoring: 1 point for isolating the term with x; 1 point for the solution.

a) Distribute: \(5x – 5 = 5x – 5\), always true: infinitely many solutions.

b) Subtract \(2x\): \(3 = -4\), always false: no solution.

Scoring: 1 point for each correct classification with support.

Equation: \(3x + 8 = 29\). Subtract 8: \(3x = 21\). Divide by 3.

\(x = 7\)

Scoring: 1 point for the equation; 1 point for the solution.

a) \(2x + 2(x + 6) = 44\).

b) \(4x + 12 = 44\), so \(4x = 32\) and \(x = 8\).

c) Width 8 in, length \(8 + 6 = 14\) in. Check: \(2(8) + 2(14) = 44\).

Width 8 inches, length 14 inches

Scoring: 1 point per part.

a) \(120 + 15w = 45 + 20w\).

b) Subtract \(15w\): \(120 = 45 + 5w\). Subtract 45: \(75 = 5w\), so \(w = 15\).

c) \(120 + 15(15) = 345\) and \(45 + 20(15) = 345\).

15 weeks; $345 each

Scoring: 1 point per part.

The student multiplied only the first term. Correct distribution: \(3x + 12 = 21\).

Subtract 12: \(3x = 9\). Divide by 3.

\(x = 3\) (the 4 must also be multiplied by 3)

Scoring: 1 point for identifying the error; 1 point for the correct solution.