To review the concept of inequality, go to Inequalities Study Guide.
Inequalities Practice Questions
Practice

Draw the solution set of x ≤ 4 on the following number line.

What inequality is represented by the graph?

What is the solution of the inequality 3x > 9?

Which of the following is the solution of the inequality –6a – 4 ≥ 8?

What compound inequality is shown in the graph?

Draw a number line for the compound inequality x > 6 or x ≤ –3.
Solutions

Create a number line for the solution to the inequality x is less than or equal to 4. This is a graph with a closed circle at 4 and the arrow pointing to the left.

In this number line, there is an open circle at –3, so the symbol in the inequality is either < or > .The arrow is pointing to the right toward numbers greater than –3. Therefore, the inequality representing the graph is y is greater than –3, which is written as y > –3.

Solve for x as you would in an equation. Divide each side of the inequality by 3: > .The solution is x > 3.

Solve for a as you would in an equation. Add 4 to both sides of the inequality.
–6a – 4 + 4 ≥ 8 + 4
–6a ≥ 12
Remember to switch the direction of the inequality symbol because you are dividing both sides by a negative number. The answer is a ≤ –2.

This graph shows that the solution set is all numbers between –4 and 9, and includes –4 because of the closed circle. In the solution set are numbers that are greater than or equal to –4 and, at the same time, less than 9.

You need to create a number line for a compound inequality that shows two inequalities at once on the same graph. The inequality x > 6 has an open circle at 6 and an arrow to the right. The other inequality, x≤ –3, has a closed circle at –3 and an arrow pointing to the left.
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