Practice Math Questions for Praxis: Solving Inequalities

By Carla Kirkland, Chan Cleveland

Problems involving inequalities on the Praxis Core exam will usually require you to do some math—but they may also involve recognizing the symbols on a number line.

In the following practice questions, you start by solving an inequality, and then you need to match the inequality to its appropriate graph on a number line.

Practice questions

  1. If9j − 13 ≥ 4j + 17

    which of the following CANNOT be the value of j?

    A. 6
    B. 7
    C. 5
    D. 9
    E. 8

  2. Which of the following graphs represents the inequality x > 4?A.





Answers and explanations

  1. The correct answer is Choice (C).

    First, get the j terms on one side of the inequality by subtracting either 9j or 4j from both sides. Then undo everything that’s being done to j by performing opposite operations on both sides:


    The last inequality has j on one side and by itself on that side, so it’s the solution. Because the value of j is either 6 or something greater than 6, only Choice (C), 5, cannot be the value of j.

  2. The correct answer is Choice (E).

    Choice (E) is a graph in which the point representing 4 has a clear circle around it, indicating that 4 is a boundary for a region of the graph but isn’t part of the region. The line is darkened infinitely to the right of 4, representing all numbers that are greater than 4.

    A darkened circle indicates that a number is included in a set, and it’s used when “or equal to”


    is involved in an inequality. Choice (D) is the graph for


    because the darkened circle shows that 4 is included in the solution set.