body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Pearson Algebra 2 Common Core, 2011

PA

Pearson Algebra 2 Common Core, 2011 View details

Get Ready!

Continue to next subchapter

Exercise 4 Page 191

Try to rewrite this inequality as a compound inequality.

Solution Set: {y | y≤- 54 or y≥ 94}
Graph:

Practice makes perfect

We are asked to find and graph the solution set for all possible values of y in the given inequality. Let's begin by isolating the absolute value in the inequality. 6|4y-2|≥ 42 ⇒ |4y-2|≥ 7 Now, we will create a compound inequality by removing the absolute value. In this case, the solution set is any number that makes the distance between 4y and 2 greater than or equal to 7 in the positive direction or in the negative direction. 4y-2 ≥ 7 or 4y-2≤ -7

Let's isolate y in both of these cases before graphing the solution set.

Case 1

We are now going to solve the first inequality.

4y-2≥7

LHS+2≥RHS+2

4y≥9

.LHS /4.≥.RHS /4.

y≥9/4

This inequality tells us that all values greater than or equal to 94 will satisfy the inequality.

Case 2

Let's now move on to the second inequality.

4y-2≤-7

LHS+2≤RHS+2

4y≤-5

.LHS /4.≤.RHS /4.

y≤-5/4

This inequality tells us that all values less than or equal to - 54 will satisfy the inequality.

Solution Set

The solution to this type of compound inequality is the combination of the solution sets. First Solution Set:& y≥ 94 Second Solution Set:& y≤ - 54 Combined Solution Set:& y≤ - 54 or y≥ 94

Graph

The graph of this inequality includes all values less than or equal to - 54 or greater than or equal to 94. We show this by keeping the endpoints closed.

Subchapter links

Exercises p.191