Question 1Easier
Which of the following is the solution of ?
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Answer: A —
Subtracting 1 gives . Dividing all three parts by 3 gives .
Study on the flyACTMathematicsInequalities (linear and compound)
Mathematics
Inequalities (linear and compound) — ACT practice questions
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What this topic is
Inequalities (linear and compound) are solved much like equations, with one key difference: multiplying or dividing both sides by a negative number reverses the inequality sign.
A compound inequality, such as x plus one lying between negative two and five, is solved by doing the same step to all three parts at once. Absolute value inequalities describe distance, so all numbers within two units of six are exactly those where the absolute value of x minus six is at most two.
Questions ask for solution sets, number-line graphs or the first whole number meeting a condition; choices often differ only by a flipped sign or a strict versus inclusive symbol.
Sample questions
Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.
Question 2Easier
Which of the following inequalities represents all real numbers whose distance from 50 is at most 3?
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Answer: A —
The expression is the distance from to 50. Requiring that distance to be at most 3 gives .
Question 3Mid
A collector’s display case holds 12 coins in its first row. Each row after that holds 7 more coins than the row before it. Which row is the first to contain more than 100 coins?
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Answer: C — 14
Row holds coins. Row 13 holds coins, and row 14 holds coins, the first total exceeding 100.
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Practice 47 Inequalities (linear and compound) questions in the app
More ACT topics
Mathematics
- Real number system and number properties
- Integer and rational exponents
- Radicals and roots
- Complex numbers
- Vectors and matrices
- Fractions, decimals, and operations
- Percents and percent change
- Ratios, rates, and proportional relationships
- Linear equations and expressions in one variable
- Systems of equations
- Polynomial expressions and factoring
- Quadratic equations
- Radical and rational equations
- Exponential relationships
- Function notation and evaluating functions
- Linear functions and graphs
- Quadratic and polynomial functions
- Radical and rational functions
- Piecewise functions
- Exponential and logarithmic functions
- Key features and transformations of graphs
- Lines, angles, and polygons
- Triangles — congruence, similarity, Pythagorean theorem
- Circles — arcs, sectors, angles, equations
- Surface area and volume of solids
- Coordinate geometry — distance, midpoint, slope, line equations
- Conic sections
- Right-triangle trigonometry and trig functions
- Measures of center and spread
- Data collection methods and study design
- Bivariate data and relationships (scatterplots, correlation)
- Probability and sample spaces
- Counting, combinations, and permutations
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