# ﻿Efficiently Solving Inequalities

Warmup

Activity #1

` Graph the Solution of an Inequality on a Number Line.` (1.) Here is an inequality: (a.) Predict what you think the solutions on the number line will look like.

• Graph its solutions on the number line below.

(2.) Here is an inequality: • Graph its solutions on the number line below.

(3.) Here is an inequality: 2x < 6 .

• Graph its solutions on the number line below.

(4.) Here is an inequality: -2x < 6 .

• Graph its solutions on the number line below.

(5.) Here is an inequality: -4x + 5 ≥ 25

• Graph its solutions on the number line below.

Activity #2

` Solve and Graph an Inequality.` (1.) Solve the following inequality and graph the solutions on the number line: (2.) Solve the following inequality and graph the solutions on the number line below: (3.) Solve the following inequality and graph the solutions on the number line below: Activity #3

` Complete an Inequality Table.` • Investigate the inequality x – 3 > -2 and complete the following table.

(i.) For which values of is it true that (ii.) For which values of is it true that • Investigate the inequality 2x < 6 and complete the following table.

(i.) Predict which values of will make the inequality 2x < 6  true.

(ii.) Does the table match your prediction?

• Investigate the inequality: -2x < 6, and complete the following table.

(i.) Predict which values of will make the inequality 2x < 6  true.

(ii.) Does the table match your prediction?

Activity #4

Investigate Inequalities on the Coordinate Plane.

The parameters in the applet below, refer to the numbers in the inequalities. They can be selected from -50 to +50. And the inequality symbols can be selected from <,  , >,  .

The inequality in the app below, defines the region below the dotted line. Note that points on the line DO NOT satisfy the inequality. • Interact with the applet below and answer the questions that follow.

(1.) Write down four pairs of points from the graph that will satisfy the inequality.

(2.) What are the coordinates of the points where the graph crosses the axes?

• You can confirm that by checking the box, “Show Intercepts”
• Slowly move the the C slider back and forth with the “Show Intercept” box checked to see other points where the graph crosses the axes.
• Play around with A and B sliders to see different slopes that the graph takes.
• Continue to move the C slider to see the intercepts.
• Change the inequality symbol and locate the region that will satisfy the inequality.

Challenge #1

Consider the inequality Predict which values of that will make the inequality true, and complete the table to check your prediction.

Challenge #2

Consider the inequality Challenge #3

Quiz Time