Click Basic Inequalities or Solving One Step Linear Inequalities for introductory information.

 If you can solve a linear equation, you can solve a linear inequality. The process is the same, with one important exception ...

 ... when you multiply (or divide) an inequality by a negative value, you must change the direction of the inequality.

Let's see why this "exception" is actually needed.

 We know that 3 is less than 7. Now, lets multiply both sides by -1. Examine the results (the products). ... written 3 < 7. ... written (-1)(3) ? (-1)(7) ... written -3 ? -7 On a number line, -3 is to the right of -7, making -3 greater than -7. -3 > -7 We have to reverse the direction of the inequality, when we multiply or divide by a negative value, in order to maintain a "true" statement.

 Solve and graph the solution set of:   4x < 24 Proceed as you would when solving a linear equation such as 4x = 24: Divide both sides by 4. Note: The direction of the inequality stays the same since we did NOT divide by a negative value. Graph using an open circle for 6 (since x can not equal 6) and an arrow to the left (since our symbol is less than).

 Solve and graph the solution set of:   -5x 25 Divide both sides by -5. Note: The direction of the inequality was reversed since we divided by a negative value. Graph using a closed circle for -5 (since x can equal -5) and an arrow to the left (since our final symbol is less than or equal to).

 Solve and graph the solution set of:   3x + 4 > 13 Proceed as you would when solving a linear equation such as 3x + 4 = 13: Subtract 4 from both sides. Divide both sides by 3. Note: The direction of the inequality stays the same since we did NOT divide by a negative value. Graph using an open circle for 3 (since x can not equal 3) and an arrow to the right (since our symbol is greater than).

 Solve and graph the solution set of:   9 - 2x 3 Subtract 9 from both sides. Divide both sides by -2. Note: The direction of the inequality was reversed since we divided by a negative value. Graph using a closed circle for 3 (since x can equal 3) and an arrow to the right (since our symbol is greater than or equal to).

 Solve and graph the solution set of:   3 - 4x + 2 13 Combine 3 and 2 on the left side. Subtract 5 from both sides. Divide both sides by -4. Note: The direction of the inequality was reversed since we divided by a negative value. Graph using a closed circle for -2 (since x can equal -2).

 Solve and graph the solution set of:   10 < 3(2x + 4) - 4x Distribute across parentheses. Combine the x-values. Subtract 12 from both sides. Divide both sides by 2. Note: There was no multiplication or division by a negative value, so the inequality symbol did not get reversed. Remember: -1 < x can be reversed so x is on the left side, and written as x > -1. Graph using a closed circle for -2 (since x can equal -2).

 Yes, there is a way to determine solutions for inequalities on your graphing calculator. Click the calculator at the right to see how to use the calculator with single variable inequalities.