Algebra 1 Practice Test: Compound Inequalities
- Compound Inequalities
- 10 questions
- 13 minutes
These 10 questions cover three-part inequalities, "or" inequalities, and cases with no solution or all real numbers. Whatever you do to one part of a three-part inequality, do it to all three parts.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
Your result
- 0 correct
- 0 wrong
- 0 blank
-
Question 1
Solve −3 < 2x + 1 ≤ 9.
Correct answer: B
Subtract 1 from all three parts: −4 < 2x ≤ 8. Divide all parts by 2: −2 < x ≤ 4. The inequality symbols keep their positions.
-
Question 2
Solve x + 3 < 1 or 2x ≥ 10.
Correct answer: D
The first part gives x < −2 and the second gives x ≥ 5. Adding 3 instead of subtracting it gives the trap x < 4.
-
Question 3
Which inequality describes all numbers between −1 and 6, including −1 but not including 6?
Correct answer: A
"Including" means the endpoint gets ≤, and "not including" means it gets <. So −1 uses ≤ and 6 uses <.
-
Question 4
Solve −5 ≤ −x + 2 < 3.
Correct answer: C
Subtract 2: −7 ≤ −x < 1. Dividing by −1 reverses both symbols: 7 ≥ x > −1, which is −1 < x ≤ 7. Not reversing gives −7 ≤ x < 1.
-
Question 5
What is the solution of x > 3 and x < 1?
Correct answer: C
An "and" inequality needs both parts to be true at once. No number is both greater than 3 and less than 1.
-
Question 6
What is the solution of x < 4 or x > −2?
Correct answer: A
An "or" statement is true if either part is true. Every number is either less than 4 or greater than −2 (most are both), so the solution is all real numbers.
-
Question 7
Which value of x satisfies 4 ≤ 3x − 2 < 13?
Correct answer: B
Add 2: 6 ≤ 3x < 15, then divide by 3: 2 ≤ x < 5. The value 2 is included, but 5 is not because of the strict <.
-
Question 8
A ride allows riders who are at least 48 inches tall and less than 76 inches tall. Which inequality describes an allowed height h?
Correct answer: D
"At least 48" means 48 is allowed (≤), and "less than 76" means 76 is not allowed (<). Both must be true, so it is an "and" inequality.
-
Question 9
How many integers satisfy −3 < x ≤ 2?
Correct answer: A
The integers are −2, −1, 0, 1 and 2. −3 is excluded by the strict <, while 2 is included.
-
Question 10
Solve 1 ≤ x + 52 ≤ 4.
Correct answer: B
Multiply all parts by 2: 2 ≤ x + 5 ≤ 8. Then subtract 5: −3 ≤ x ≤ 3. Subtracting 5 before multiplying gives the wrong interval −8 ≤ x ≤ −2.
Questions you leave blank are not counted as wrong.
More Math tests
MathAlgebra 1 Practice Test: Slope-Intercept and Point-Slope FormSlope-Intercept and Point-Slope Form10 questions13 min MathAlgebra 1 Practice Test: Solving Linear Equations and InequalitiesSolving Linear Equations and Inequalities15 questions20 minMathAlgebra 1 Practice Test: Linear Functions, Slope and GraphsLinear Functions, Slope and Graphs15 questions20 minMathAlgebra 1 Practice Test: Systems of Equations and InequalitiesSystems of Equations and Inequalities15 questions20 minMathAlgebra 1 Practice Test: Exponents, Polynomials and FactoringExponents, Polynomials and Factoring15 questions20 minMathAlgebra 1 Practice Test: Quadratic Equations and FunctionsQuadratic Equations and Functions15 questions20 minMathAlgebra 1 Practice Test: Literal EquationsLiteral Equations10 questions13 min