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McGraw Hill Glencoe Algebra 1, 2012 View details

6. Graphing Inequalities in Two Variables

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Exercise 55 Page 322

Try to rewrite this inequality as a compound inequality.

{y | y>6 or y<-2 }

Practice makes perfect

We are asked to find the solution set for all possible values of y in the given inequality. |y-2| > 4 To do this, 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 y and 2 greater than 4 in the positive direction or in the negative direction.

y-2 >4 or y-2< - 4 Let's isolate y in both of these cases before determining the solution set.

Case 1

y-2>4

AddIneq

LHS+2>RHS+2

y>6

This inequality tells us that all values greater than 6 will satisfy the inequality.

Case 2

y-2<-4

AddIneq

LHS+2

y<-2

This inequality tells us that all values less than -2 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>6 Second Solution Set:& y<-2 Combined Solution Set:& y>6 or y<-2

Subchapter links

Check Your Understanding p.320

Practice and Problem Solving p.320-321

H.O.T. Problems p.321

Standardized Test Practice p.322

Spiral Review p.322

Skills Review p.322

Exercise 55 Page 322

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Check the answer

Practice exercises

Asses your skill

Case 1

Case 2

Solution Set