Please login now to access the My Options Box.  If you don't already have an account with us, click on the Free Registration link
The My College Options® Resource Center provides up to date news and information for students and parents.
Test PrepSATMathInequalities

SAT Math Skill Review: Inequalities

An inequality is a statement indicating that one quantity is greater than or less than another. Inequalities are shown using four symbols:





Greater than

Greater than or equal to


Less than

Less than or equal to

Solving inequalities works just like solving an equality (an equation with an “=” sign), except for one important difference:

When multiplying or dividing an inequality by a negative number, you must switch the sign.

Let’s take a look at an example:

Your first step is to isolate the variable. To do this, add 5 to each side:

Next, divide both sides by 2. Because 2 is a positive number, you don’t need to worry about switching the signs:

This expression means that all values of x that are greater than 7 are solutions to this inequality.


  1. Solve the inequality 3x + 5 < 5x - 9

    (A) x > 7
    (B) x < 7
    (C) x > 2
    (D) x < 2
    (E) x = 7

  2. Which of the following algebraic inequalities is represented by the graph below?

    (A) -2 ≥ y < 2
    (B) -2 < y > 2
    (C) -2 ≤ y < 2
    (D) -2 < y ≤ 2
    (E) -2 ≤ y ≤ 2

Answers and Explanations

  1. The correct answer is A. First, subtract 5 from both sides to get 3x < 5x – 14. Then, subtract 5x from both sides to get -2x < -14. To solve for x, divide both sides by -2 and, since you are dividing by a negative number, switch the inequality sign to get your final solution: x > 7. Notice that the test-writers also give you x < 7 as an answer choice, so don’t forget to switch the inequality sign!
  2. The correct answer is C. The graph represents a line whose solution y lies between -2 and 2. The filled point represents a true value for y. Based on the graph, y = -2. This allows you to eliminate choices B and D which don’t allow for this value. The open point represents y ≠ 2. This allows you to eliminate choices D and E. To answer the question, you must combine the two inequalities into one statement: -2 ≤ y < 2. Only choices A and C remain to check.  

More Resources


Thank you for visiting

My College Options® is an online college planning program that connects millions of high school students with colleges and universities.

Please email us at to find out if your institution is doing everything it can to reach qualified, prospective students. We look forward to hearing from you.

To learn more about the tools and resources available to you, click here


Don Munce