How to Solve My Inequality & Graph it on a Number Line

Linear inequalities have many similarities to linear equations. Linear inequalities and linear equations differ in that equations have one solution, whereas inequalities have a range of solutions. If you can solve an equation, you can quickly learn how to solve an inequality. Linear inequalities can also be graphically represented on a number line.

Instructions

Solving Inequalities

1. Add or subtract expressions in an inequality as you would with a linear equation, aiming to isolate your variable. For example, to solve 2x-4>12, you can add 4 to both sides and have 2x>16.

2. Multiply or divide positive numbers in an inequality as you would with a linear equation, with the goal of isolating your variable. For example, simply 2x>16 by dividing both sides by 2, equaling x>8.

3. Flip the inequality sign when you multiply or divide by a negative number. For example, to solve -4x>12, divide both sides by -4 and flip the sign, equaling x<-3.

Graphing Inequalities on a Number Line

1. Draw a number line.

2. Locate the number which your inequality is greater or less than. If you are graphing x>3, for example, locate 3.

3. Draw an open circle if your inequality does not include that value. If x is greater than three, for example, you would use an open circle. Draw a shaded circle if your inequality includes that value. For example, to graph x is greater than or equal to three, you would draw a shaded circle.

4. Darken the portion of the number line that is left to the value if x is less than that value. Darken the portion of the number line that is right to the value if x is greater than that value.

Tips & Warnings

• Always remember to flip the inequality sign when multiplying or dividing by a negative number.

References

• West Texas A&M: Solving Linear Inequalities
• Purple Math: Solving Inequalities, An Overview
• Purple Math: Solving Linear Inequalities, Introduction and Formatting