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Accuplacer Linear and Absolute Value Inequalities — practice questions

Explore 6 free Linear and Absolute Value Inequalities questions in Accuplacer Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Linear and Absolute Value Inequalities questions and exercises with answers

Showing questions 1–6 of 6.

In interval notation, what does a square bracket next to a number mean?Read the answer and worked solution →Which single step in solving an inequality forces the inequality sign to flip?Read the answer and worked solution →Solve the compound inequality 4 less than 2x minus 8, which is less than or equal to 10.Read the answer and worked solution →Write the solution of the absolute value inequality the absolute value of (x - 7) less than or equal to 3.Read the answer and worked solution →Catch the slip in each inequality lineRead the answer and worked solution →Match each interval to what it holdsRead the answer and worked solution →

Worked practice questions

In interval notation, what does a square bracket next to a number mean?

  1. That number is left out
  2. That number is included
  3. That number is negative
  4. That number is a limit
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Correct answer: B. That number is included

1. Interval notation marks each end of a solution set with either a bracket or a parenthesis. 2. A bracket marks an endpoint that belongs to the set, matching a greater than or equal to sign. 3. A parenthesis marks an endpoint left out of the set, and infinity always takes a parenthesis. _Source: OpenStax College Algebra (CC BY 4.0), section 2.7 Linear Inequalities and Absolute Value Inequalities_

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Which single step in solving an inequality forces the inequality sign to flip?

  1. Adding a negative number
  2. Dividing by a negative
  3. Subtracting a variable term
  4. Multiplying by a positive
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Correct answer: B. Dividing by a negative

1. Adding or subtracting the same amount on both sides never disturbs the direction of an inequality. 2. Multiplying or dividing by a positive number leaves the direction alone as well. 3. Multiplying or dividing by a negative number reverses the order of the two sides. 4. So the inequality symbol must be flipped at exactly that step. _Source: OpenStax College Algebra (CC BY 4.0), section 2.7 Linear Inequalities and Absolute Value Inequalities_

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Solve the compound inequality 4 less than 2x minus 8, which is less than or equal to 10.

  1. The interval [6, 9)
  2. The interval (2, 5]
  3. The interval (6, 9]
  4. The interval (6, 18]
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Correct answer: C. The interval (6, 9]

1. A compound inequality can be solved by working on all three parts at once. 2. Add 8 to every part to undo the subtraction. 3. That turns 4 into 12, leaves 2x in the middle, and turns 10 into 18. 4. Now divide every part by 2. 5. That gives 6 on the left, x in the middle, and 9 on the right. 6. The left sign was strictly less than, so 6 is left out and takes a parenthesis. 7. The right sign was less than or equal to, so 9 is included and takes a bracket. 8. The solution is therefore the interval from 6 to 9, written (6, 9]. 9. The interval [6, 9) swaps the two endpoint symbols. 10. The interval (6, 18] forgets the final division by 2 on the right end. _Source: OpenStax College Algebra (CC BY 4.0), section 2.7 Linear Inequalities and Absolute Value Inequalities_

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