Big Ideas Math Integrated I, 2016
BI
Big Ideas Math Integrated I, 2016 View details
3. Function Notation
Continue to next subchapter

Exercise 39 Page 126

Split the compound inequality into two separate inequalities.

Solution Set: -3< k<-1/3
Graph:

Practice makes perfect
We were asked to solve a compound inequality. Let's start by splitting it into separate inequalities. Compound Inequality: -16< 6k&+2 < 0 First Inequality: -16< 6k&+2 Second Inequality: 6k&+2 < 0 Notice that compound inequalities written in this way are equivalent to compound inequalities that involve the word "and." -16< 6k+2 and 6k+2< 0

Let's solve the inequalities separately.

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 we divide or multiply by a negative number, we must flip the inequality sign.
-16 < 6k+2
â–Ľ
Solve for k
-16- 2 < 6k+2- 2
-18 < 6k
-18/6 < 6k/6
-18/6 < 6k/6
-3 < 6k/6
-3 < 6/6 * k
-3 < 1 * k
-3 < k
This inequality tells us that all values greater than -3 will satisfy the inequality.

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

Second Inequality

Once more, we will solve the inequality by isolating the variable.
6k+2 < 0
â–Ľ
Solve for k
6k+2- 2 < 0- 2
6k<-2
6k/6 < -2/6
6/6 * k < -2/6
1 * k < -2/6
k < -2/6
k<-2/6
k<-2/ 2/6/ 2
k<-1/3
This inequality tells us that all values less than -1/3 will satisfy the inequality.

Note that the point on - 13 is open because it is not included in the solution set.

Compound Inequality

The solution to the compound inequality is the intersection of the solution sets. First Solution Set: -3< k& Second Solution Set: k&< - 13 Intersecting Solution Set: -3< k & < - 13 Finally, we will graph the solution set to the compound inequality on a number line.