How Do You Solve Linear Inequalities?

How Do You Solve Linear Inequalities?

To solve a linear inequality, find the constant on a number line, and either fill it in or circle it, depending on the nature of the inequality. Next, draw an arrow pointing in the direction indicating that the inequality is "greater than" (>) or "less than" (<) the constant.

  1. Draw a number line surrounding your constant

    Consider the example problem x > -8. Draw a horizontal line with an arrow on each end, and mark off small vertical lines for each integer from -12 to -4, getting more positive (and closer to zero) as you move from left to right, to provide plenty of integers on either side of the constant in the problem (-8).

  2. Indicate the nature of the inequality

    Circle the vertical line corresponding to (-8). Remember that the circle means that the inequality does not include the constant itself as a possible solution. Fill in the circle when the < or > sign has an underscore beneath it, which means the notation is "greater (or less) than or equal to."

  3. Draw an arrow in the appropriate direction

    Draw an arrow to the right along the number line, starting at the circle and going to the right end of the number line to show the inequality is "greater than" (-8). Add an arrow head to the end of the line to show that the line goes on to infinity, as all numbers in that direction are a part of the solution. Draw an arrow to the left when the inequality includes solutions "less than" the constant.