Efficiently Solving Inequalities: IM 7.6.15
[url=https://im.kendallhunt.com/MS/teachers/2/6/15/preparation.html]“Efficiently Solving Inequalities”[/url] from IM Grade 7 by [url=https://www.geogebra.org/m/gus8ffvr]Open Up Resources[/url] and Illustrative Mathematics. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0 license[/url].
Table of Contents
- Lesson 7.6.15
- IM 7.6.15 Lesson: Efficiently Solving Inequalities
- Practice 7.6.15
- IM 7.6.15 Practice: Efficiently Solving Inequalities
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]:
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.
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 Practice: Efficiently Solving Inequalities
[size=150]Consider the inequality [math]-1\le\frac{x}{2}[/math].[br][/size][br]Predict which values of [math]x[/math] will make the inequality true.
Complete the table to check your prediction.
[size=150]Consider the inequality [math]1\le\frac{-x}{2}[/math].[br][/size][br]Predict which values of [math]x[/math] will make the inequality true.
Complete the table to check your prediction.
Diego is solving the inequality [math]100-3x\ge-50[/math]. He solves the equation [math]100-3x=-50[/math] and gets [math]x=50[/math]. What is the solution to the inequality?
[size=150]Solve the inequality [math]-5\left(x-1\right)>-40[/math].[/size]
Graph the solution on a number line.
Select [b]all[/b] of the values that make the inequality [math]-x+6\ge10[/math] true.
Draw the solution set for each of the following inequalities: x > 7
Draw the solution set for each of the following inequalities: x ≥ -4.2
The price of a pair of earrings is $22 but Priya buys them on sale for $13.20.
By how much was the price discounted?
What was the percentage of the discount?