Linear Inequalities Test Answer Key with Scoring – Algebra 1

Question 1 One inequality (2 points)

Add 7: 4x ≥ 20. Divide by 4: x ≥ 5.

x ≥ 5

Scoring: 1 point for the solution, 1 point for a correct graph.

Question 2 Negative divisor (2 points)

Subtract 5: −3x < 12. Divide by −3 and reverse the sign: x > −4.

x > −4

Scoring: 1 point for isolating −3x, 1 point for the reversed sign and answer.

Question 3 Distribute and compare (2 points)

4x + 12 ≥ 7x − 9. Subtract 4x: 12 ≥ 3x − 9. Add 9: 21 ≥ 3x. So x ≤ 7.

x ≤ 7

Scoring: 1 point for distributing and collecting terms, 1 point for the answer.

Question 4 An and inequality (2 points)

Subtract 1: −6 ≤ 3x < 15. Divide by 3: −2 ≤ x < 5.

−2 ≤ x < 5, or [−2, 5)

Scoring: 1 point for the compound solution, 1 point for the notation.

Question 5 An or inequality (2 points)

First: 2x ≤ −6, so x ≤ −3. Second: x > 4.

x ≤ −3 or x > 4, or (−∞, −3] ∪ (4, ∞)

Scoring: 1 point per part.

Question 6 Read the segment (2 points)

Open at −6 and closed at 1.

−6 < x ≤ 1, or (−6, 1]

Scoring: 1 point for the inequality, 1 point for the interval notation.

Question 7 Read the ray (2 points)

Closed at 3 with the shading to the right: x ≥ 3.

Solution example: 3 (or 10). Non-solution example: 2.

x ≥ 3

Scoring: 1 point for the inequality, 1 point for correct examples.

Question 8 Band fundraiser (3 points)

(a) 420 + 4.5b ≥ 1,500.

(b) 4.5b ≥ 1,080, so b ≥ 240.

(c) 240 boxes give exactly $1,500.

At least 240 boxes

Scoring: 1 point per part.

Question 9 Daily calories (3 points)

(a) 2,200 ≤ 600 + 180n ≤ 3,000.

(b) 1,600 ≤ 180n ≤ 2,400, so 8.89 ≤ n ≤ 13.33 (rounded).

(c) Whole numbers: 9, 10, 11, 12, 13.

Check: 9 bars give 2,220 and 13 bars give 2,940.

9 to 13 bars

Scoring: 1 point per part.