Exercise 26 Page 46

To do this, we will create a compound inequality by removing the absolute value. In this case, the solution set is any number less than 18 away from the midpoint in the positive direction and any number less than 18 away from the midpoint in the negative direction. Absolute Value Inequality:& |6y-2| < 18 Compound Inequality:& - 18< 6y-2 < 18 We can split this compound inequality into two cases, one where 6y-2 is greater than -18 and one where 6y-2 is less than 18. - 18< 6y-2 and 6y-2< 18 Let's isolate y in both of these cases before graphing the solution set.

Case 1

Case 2

- 18<6y-2

AddIneq

LHS+2

-16<6y

DivIneq

.LHS /6.<.RHS /6.

-16/6

ReduceFrac

a/b=.a /2./.b /2.

-8/3

RearrangeIneq

Rearrange inequality

y> -8/3

This inequality tells us that all values greater than - 83 will satisfy the inequality.

Solution Set

The solution to this type of compound inequality is the overlap of the solution sets. Let's recombine our cases back into one compound inequality. First Solution Set:& y < 10/3 Second Solution Set:& -8/3 < y Intersecting Solution Set:& -8/3 < y < 10/3

Graph

The graph of this inequality includes all values from - 83 to 103, not inclusive. We show this by using open circles on the endpoints.