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Pearson Algebra 1 Common Core, 2011 View details

2. Solving Inequalities Using Addition or Subtraction

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Exercise 22 Page 174

What can you do to isolate a variable in an inequality?

Solution Set: z≤8
Graph:

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 you divide or multiply by a negative number, you must reverse the inequality sign.

z-12≤-4

AddIneq

LHS+12≤RHS+12

z≤8

The above tells us that all values less than or equal to 8 will satisfy the inequality. Below we demonstrate the inequality by graphing the solution set on a number line. Notice that z can equal 8, which we show with a closed circle on the number line.

Checking Our Solution

We can check our solution by substituting a few values into the given inequality. The value satisfies the inequality if the inequality remains true after substituting and simplifying.

z	z-12≤-4	Evaluate
7	7-12≤-4	- 5≤ - 4
8	8-12≤-4	- 4 ≤ - 4
9	9-12≤-4	- 3 ≰ - 4

We can conclude that, as long as z is less than or equal to 8, the inequality is satisfied.

Subchapter links

Lesson Check p.174

Practice and Problem-Solving Exercises p.174-177

Standardized Test Prep p.177

Mixed Review p.177

Exercise 22 Page 174

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