How to Solving Linear Inequalities – Step by Step Guide with Examples

solution of a linear inequality

is any ordered pair that makes the inequality true.

To solve a linear inequality, follow these steps:

1. Identify the variable. The variable is the letter used to represent an unknown value in an equation or inequality. Let’s say the variable is x.

2. Isolate the variable on one side of the inequality. Similar to the process of solving an equation, you want to get all the x terms on one side of the inequality and all the constant terms on the other side. However, there’s one big difference from equations: when you multiply or divide both sides of an inequality by a negative number, you must flip the inequality symbol. Here are some examples:

a. x + 5 < 10 Subtract 5 from both sides to isolate x: x < 5 b. 3x - 4 ≤ 5x + 10 Subtract 3x from both sides to isolate the variable: -4 ≤ 2x + 10 Subtract 10 from both sides to isolate the x term: -14 ≤ 2x Divide both sides by 2, but note that we need to flip the inequality since we divided by a negative number: -7 ≥ x or x ≤ -7 3. Graph the solution on a number line. A number line is a visual way to represent the solution set of an inequality. Open circles ( ) represent values that are not included in the solution set (because the inequality is less than or greater than), while closed circles [ ] represent values that are included in the solution set (because the inequality is less than or equal to or greater than or equal to). For example, if x > 3, you would graph an open circle at 3 and then shade to the right because all values greater than 3 satisfy the inequality.

4. Check the solution. To check if a value satisfies an inequality, simply plug it in and see if the inequality is true. If it is, then that value is included in the solution set. If it’s not, then that value is not included in the solution set.

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