Linear Equations Test Answer Key with Scoring – Algebra 1

Question 1 Variables on both sides (2 points)

5x − 13 = 22, so 5x = 35 and x = 7.

Check: 8(7) − 13 = 43 and 3(7) + 22 = 43.

x = 7

Scoring: 1 point for correct algebra, 1 point for the answer with a check.

Question 2 Distribute and combine (2 points)

6x − 8 − 5 = 15 − x, so 6x − 13 = 15 − x.

7x = 28, so x = 4.

Check: 2(8) − 5 = 11 and 15 − 4 = 11.

x = 4

Scoring: 1 point for distributing and combining like terms, 1 point for the solution.

Question 3 Equation with fractions (2 points)

Multiply every term by 6: 2x − 3 = 5. Then 2x = 8 and x = 4.

Check: 4/3 − 1/2 = 8/6 − 3/6 = 5/6.

x = 4

Scoring: 1 point for clearing fractions, 1 point for the solution.

Question 4 Justify the steps (2 points)

5x + 9 = 3x − 7 (given)

2x + 9 = −7 (subtraction property of equality: subtract 3x)

2x = −16 (subtraction property: subtract 9)

x = −8 (division property of equality: divide by 2)

x = −8

Scoring: 1 point for the solution, 1 point for correct reasons.

Question 5 Number of solutions (2 points)

(a) 6x + 15 = 6x + 11 gives 15 = 11, false: no solution.

(b) 4x − 8 = 4x − 8 is always true: infinitely many solutions.

Scoring: 1 point per part.

Question 6 Moving company (3 points)

(a) 90 + 35h = 50 + 45h.

(b) 40 = 10h, so h = 4.

(c) 90 + 35(4) = 230.

4 hours; $230

Scoring: 1 point per part.

Question 7 Pyramid volume formula (3 points)

(a) Multiply by 3: 3V = Bh. Divide by B: h = 3V/B.

(b) h = 3(96)/36 = 288/36 = 8.

h = 3V/B; h = 8

Scoring: (a) 1 point for multiplying by 3, 1 for dividing by B; (b) 1 point.

Question 8 Perimeter of a triangle (2 points)

x + (x + 6) + (2x − 2) = 40, so 4x + 4 = 40 and x = 9.

Sides: 9, 15, 16.

x = 9; sides 9, 15, 16 cm

Scoring: 1 point for the equation and x, 1 point for all sides.

Question 9 Simple interest (2 points)

(a) Divide both sides by Pt: r = I/(Pt).

(b) r = 135/(1,500 × 3) = 135/4,500 = 0.03 = 3%.

r = I/(Pt); 3%

Scoring: 1 point per part.