IM 7.6.15 Lesson: Efficiently Solving Inequalities

Here is an inequality: -x ≥ -4. Predict what you think the solutions on the number line will look like.

Select [b]all [/b]the values that are solutions to [math]-x\ge-4[/math]:

[math]4.001[/math] [math]3[/math] [math]-4.001[/math] [math]-4[/math] [math]-3[/math] [math]4[/math]

Graph the solutions to the inequality in the previous question on the number line: -x ≥ -4

Let's investigate the inequality x - 3 > -2. Complete the table.

For which values of [math]x[/math] is it true that [math]x-3=-2[/math]?

For which values of [math]x[/math] is it true that [math]x-3>-2[/math]?

Graph the solutions to x - 3 > -2 on the number line:

[size=150]Here is an inequality: [math]2x<6[/math].[/size][br][br]Predict which values of [math]x[/math] will make the inequality [math]2x<6[/math] true.

Using the inequality: 2x < 6, complete the table.

Does the table match your prediction?

Graph the solutions to 2x < 6 on the number line:

[size=150]Here is an inequality: [math]-2x<6[/math].[/size][br][br]Predict which values of [math]x[/math] will make the inequality [math]-2x<6[/math] true.

Using the inequality: -2x < 6, complete the table.

Does the table match your prediction?

Graph the solutions to -2x < 6 on the number line:

How are the solutions to [math]2x<6[/math] different from the solutions to [math]-2x<6[/math]?

[size=150]Let's investigate: [math]-4x+5\ge25[/math][/size][br][br]Solve [math]-4x+5=25[/math].

Is [math]-4x+5\ge25[/math] true when [math]x[/math] is 0? What about when [math]x[/math] is 7? What about when [math]x[/math] is -7?

Graph the solutions to -4x+5 ≥ 25 on the number line.

[size=150]Let's investigate [math]\frac{4}{3}x+3<\frac{23}{3}[/math].[/size][br][br]Solve [math]\frac{4}{3}x+3=\frac{23}{3}[/math].

Is [math]\frac{4}{3}x+3<\frac{23}{3}[/math] true when [math]x[/math] is 0?

Graph the solutions to the inequality on the number line.

Solve the inequality shown and graph the solutions on the number line.

Write at least [b]three [/b]different inequalities whose solution is [math]x>-10[/math]. Find one with [math]x[/math] on the left side that uses a [math]<[/math].

IM 7.6.15 Lesson: Efficiently Solving Inequalities

Here is an inequality: -x ≥ -4. Predict what you think the solutions on the number line will look like.

Graph the solutions to the inequality in the previous question on the number line: -x ≥ -4

Let's investigate the inequality x - 3 > -2. Complete the table.

Graph the solutions to x - 3 > -2 on the number line:

Using the inequality: 2x < 6, complete the table.

Graph the solutions to 2x < 6 on the number line:

Using the inequality: -2x < 6, complete the table.

Graph the solutions to -2x < 6 on the number line:

Graph the solutions to -4x+5 ≥ 25 on the number line.

Graph the solutions to the inequality on the number line.

Solve the inequality shown and graph the solutions on the number line.

Solve the inequality shown and graph the solutions on the number line.

Information: IM 7.6.15 Lesson: Efficiently Solving Inequalities