Envision Math 2.0: Grade 7, Volume 2
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Envision Math 2.0: Grade 7, Volume 2 View details
4. Solve Inequalities Using Addition or Subtraction
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Exercise 4 Page 276

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. Let's use the Subtraction Property of Inequality.

x + 5 > 3
x + 5 - 5 > 3 - 5
x > - 2

The above tells us that all values of x that are greater than - 2 will satisfy the inequality. Below we demonstrate the inequality by graphing the solution set on a number line. Notice that x can not equal - 2, which we show with an open circle on the number line.

Let's use the Subtraction Property of Inequality to solve the given inequality.

x + 5 ≤ 3
x + 5 - 5 ≤ 3 - 5
x ≤ - 2

The above tells us that all values of x that are less than or equal - 2 will satisfy the inequality. Below we demonstrate the inequality by graphing the solution set on a number line. Notice that x can equal - 2, which we show with a closed circle on the number line.

Let's use the Addition Property of Inequality to solve the given inequality.

x - 3/2 < - 3
x - 3/2 + 3/2< - 3 + 3/2
x - 3/2 + 3/2< - 6/2 + 3/2
x < - 3/2
x < - 2/2 - 1/2
x < - 1 - 1/2
x< - 1 12

The above tells us that all values of x that are less than - 1 12 will satisfy the inequality. Below we demonstrate the inequality by graphing the solution set on a number line. Notice that x can not equal - 1 12, which we show with an open circle on the number line.