solve the inequality.then graph the solution set |x-8|-8 less then equal to -3

Question

Solve the inequality, then graph the solution set |x-8|-8 less then equal to -3

Answer 1

Absolute value inequalities/equations always need to be worked in 2 parts : 1 for the expression within the | | as-is and the other for the opposite of the expression within the | |.

 

For both, isolate the | | .

|x-8| <= -3 + 8

|x-8| <= 5

 

Then, for

 

Part 1 of 2:  Change the | | to ( ) and solve:

 

(x-8) <=5

 x-8   <=5

 x      <=5+8

x <= 13

 

Part 2 of 2: Change the | | to -( ) and solve:

 

-(x-8) <= 5

-x+8  <= 5

-x      <= 5-8

-x      <= -3

x  >= 3         <==multiplying or dividing both sides by a negative "flips" the inequality

 

Combine the answers from Parts 1 & 2:

 

  3 <= x <=13

 

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