Algebra 1 Linear Inequalities in One Variable Test Solutions and Scoring (PDF)
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.
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]
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]
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
20 points
Key facts behind this linear inequalities test answers
- 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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