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Big Ideas Math Algebra 1, 2015

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Big Ideas Math Algebra 1, 2015 View details

5. Solving Compound Inequalities

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Exercise 20 Page 85

Since the word between the inequalities is or, we are looking for the union of the solution sets of the individual inequalities.

Solution Set: b<-3 or b ≥ 5
Graph:

Practice makes perfect

To solve the compound inequality, we have to solve each of the inequalities separately. Since the word between the individual inequalities is or, the solution set for the compound inequality is the union of the individual solution sets.

First Inequality

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.

35<7(2-b)

.LHS /7.=.RHS /7.

5<2-b

LHS-2

3<- b

Multiply by -1 and flip inequality sign

-3>b

Rearrange inequality

b<-3

The above tells us that all values less than -3 will satisfy the inequality.

Strict Inequality

Note that the point on -3 is open because it is not included in the solution set.

Second Inequality

Again, we will solve the inequality by isolating the variable.

1/3(15b-12)≥ 21

LHS* 3 ≥ RHS * 3

3*1/3(15b-12)≥ 63

▼

Simplify left-hand side

MoveLeftFacToNumOne

a* 1/b= a/b

3/3(15b-12)≥ 63

a/a=1

1(15b-12)≥ 63

Identity Property of Multiplication

15b-12≥ 63

LHS+12≥RHS+12

15b ≥ 75

.LHS /15.≥.RHS /15.

b≥ 5

We found that all values greater than or equal to 5 will satisfy the inequality.

Non-Strict Inequality

Note that the point on 5 is closed because it is included in the solution set.

Compound Inequality

The solution set to the compound inequality is the union of the solution sets. First Solution Set:& b< - 3 Second Solution Set:& b≥5 Combined Solution Set:& b<-3or b≥ 5 Finally, we will graph the solution set to the compound inequality.

Or Compound Inequality

Subchapter links

Communicate Your Answer p.81

Monitoring Progress p.82-84