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

Algebra 1 math test solutions: Linear Inequalities in One Variable – Maths PDF

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This linear inequalities test answers for Algebra 1 covers linear inequalities in one variable (Common Core A-REI.B.3, A-CED.A.1), with a free PDF to print.

Linear inequalities test answers (Algebra 1) – first page of the printable PDF

Use this key to grade the linear inequalities test. Each solution shows the full work, and the scoring note explains how the points are awarded. The test totals 20 points. Give partial credit for correct steps, even when the final answer is wrong.

Algebra 1 · Common Core State Standards: A-REI.B.3, A-CED.A.1

Linear inequalities test answers: worked solutions

Question 1 – Graphs and inequalities [2 pts]

Graph of $x \ge 2$.

a) The circle at -1 is open and the ray points left: $x < -1$.

b) Closed circle at 2, ray to the right.

Scoring: 1 point for each correct part.

Question 2 – Two-step inequality [2 pts]

Add 7: $4x > 20$. Divide by 4.

$x > 5$

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

Question 3 – Negative coefficient [2 pts]

Subtract 3: $-5x \le 25$. Divide by $-5$ and reverse the symbol.

$x \ge -5$

Scoring: 1 point for the correct first step; 1 point for reversing the symbol.

Question 4 – Variables on both sides [2 pts]

Distribute: $3x + 6 \ge 5x – 4$. Subtract $3x$: $6 \ge 2x – 4$. Add 4: $10 \ge 2x$.

Divide by 2: $5 \ge x$, which is $x \le 5$.

Scoring: 1 point for distributing and collecting terms; 1 point for the final inequality written correctly.

Question 5 – And inequality [2 pts]

Graph of $2 < x < 5$.

Add 5 to all parts: $6 < 3x < 15$. Divide by 3: $2 < x < 5$.

Scoring: 1 point for the solution; 1 point for the graph with open circles.

Question 6 – Or inequality [2 pts]

First: $2x \le -4$, so $x \le -2$. Second: $x > 5$.

$x \le -2 \text{ or } x > 5$

Scoring: 1 point for each correct inequality.

Question 7 – Savings goal [3 pts]

a) $35 + 8w \ge 120$.

b) $8w \ge 85$, so $w \ge 10.625$.

c) Weeks are whole numbers, so round up. Check: 10 weeks give $115, which is not enough; 11 weeks give $123.

11 weeks

Scoring: 1 point per part.

Question 8 – Find the error [3 pts]

a) The student divided by $-4$ but did not reverse the symbol.

b) $x > -5$.

c) Test $x = 0$: $-4(0) = 0 < 20$ is true, and 0 is in the solution set $x > -5$. Test $x = -6$: $-4(-6) = 24 < 20$ is false.

Scoring: 1 point per part.

Question 9 – Test values [2 pts]

Substitute each value: $x = -1:\quad -5 < 7$ true; $x = 4: 5 < 7$ true; $x = 5: 7 < 7$ false; $x = 8: 13 < 7$ false.

$x = -1$ and $x = 4$

Scoring: 1 point for substituting all four values; 1 point for the correct two values.

Total score

Total

20 points

Key facts behind this linear inequalities test answers

Key facts

Use an open circle for < and >, and a closed circle for ≤ and ≥.
Adding or subtracting the same number never changes the inequality symbol.
Multiplying or dividing both sides by a negative number reverses the symbol.
An and inequality is true between endpoints; an or inequality is true on two rays.
“At least” means ≥ and “at most” means ≤.

How to use this linear inequalities test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

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

Linear inequalities test answers: worked solutions

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Key facts behind this linear inequalities test answers

How to use this linear inequalities test answers

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