Envision Math 2.0: Grade 7, Volume 2
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Envision Math 2.0: Grade 7, Volume 2 View details
5. Solve Inequalities Using Multiplication or Division
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Exercise 4 Page 282

Practice makes perfect
Inequalities can be solved in the same way as equations, by performing inverse operations on both sides until the variable is isolated. The only difference is that when we divide or multiply by a negative number, we must reverse the inequality sign.
4x > 12
4x/4 > 12/4
x > 3
The above tells us that all values of x that are greater than 3 will satisfy the inequality. Below we demonstrate the inequality by graphing the solution set on a number line. Notice that x can not equal 3, which we show with an open circle on the number line.
To solve the given inequality, we will use the Multiplication Property of Inequality.
x/4 ≤ - 12
x/4* 4 ≤ - 12 * 4
x ≤ - 12 * 4
x ≤ - 48
The above tells us that all values of x that are less than or equal to - 48 will satisfy the inequality. Below we demonstrate the inequality by graphing the solution set on a number line. Notice that x can equal - 48, which we show with a closed circle on the number line.
To solve the given inequality, we will use the Division Property of Inequality. When dividing both sides of inequality by a negative number, we must reverse the inequality sign.
- 4x > 12
- 4x/- 4 < 12/- 4
- 4x/- 4 < - 12/4
x < - 3
The above tells us that all values of x that are less than - 3 will satisfy the inequality. Below we demonstrate the inequality by graphing the solution set on a number line. Notice that x can not equal - 3, which we show with an open circle on the number line.