Algebra 1 Linear Inequalities in One Variable Test with Point Values (PDF)

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

This linear inequalities test 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 (Algebra 1) – first page of the printable PDF
This 45-minute test on linear inequalities covers Common Core A-REI.B.3 and A-CED.A.1 and is worth 20 points. Work alone, show all steps, and use a calculator only if your teacher allows it. Partial credit is given for correct work, so write down your reasoning even when you are unsure of the final answer.

Time and points

About this test
  • Grade: Algebra 1
  • Chapter: Linear Inequalities in One Variable
  • Standards: A-REI.B.3, A-CED.A.1
  • Time: 45 minutes
  • Total: 20 points

Linear inequalities test: questions

Question 1 – Graphs and inequalities [2 pts]

-6-5-4-3-2-10123456
Graph for question 1a.
  1. Write the inequality shown by the graph. (1 point)
  2. Graph \(x \ge 2\) on a number line. (1 point)

Question 2 – Two-step inequality [2 pts]

Solve \(4x – 7 > 13\).

Question 3 – Negative coefficient [2 pts]

Solve \(-5x + 3 \le 28\).

Question 4 – Variables on both sides [2 pts]

Solve \(3(x + 2) \ge 5x – 4\).

Question 5 – And inequality [2 pts]

Solve \(1 < 3x - 5 < 10\) and graph the solution.

Question 6 – Or inequality [2 pts]

Solve \(2x + 1 \le -3 \text{ or } x – 4 > 1\).

Question 7 – Savings goal [3 pts]

WeeksSavings0$355$7510$115
Ethan’s savings.

Ethan has $35 and saves $8 each week. He wants at least $120.

  1. Write an inequality for the number of weeks \(w\). (1 point)
  2. Solve the inequality. (1 point)
  3. State the least whole number of weeks. (1 point)

Question 8 – Find the error [3 pts]

A student solved \(-4x < 20\) and wrote \(x < -5\).

  1. Describe the error. (1 point)
  2. Write the correct solution. (1 point)
  3. Check the correct solution with a test value. (1 point)

Question 9 – Test values [2 pts]

-2-1012345678-1458
Test these values.

For which of the marked values is \(2x – 3 < 7\) true? Show your work.

View solution

Key facts behind this linear inequalities test

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

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

Prepare for the test

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