Problem: |2x+3|>5

Question

I need to solve and find domain

Answer 1

Every absolute value problem is two problems built into one.

|2x + 3| > 5 means:

a) (2x + 3) > 5 and

b) -(2x + 3) > 5

because the absolute value symbols "strip away the negative sign"

Example: |7| = 7 and |-7| = 7

So to solve |2x + 3| > 5 we look at the two cases:

Case 1

(2x + 3) > 5

2x + 3 > 5

2x > 2

x > 1

Case 1

-(2x + 3) > 5

-2x - 3 > 5

-2x > 8

x < -4 (remember that when multiplying or dividing by a negative, we must flip the sign)

So the solution is x < -4 or x > 1

The domain is all the values of "x" that make the inequality a true statement. so that would be:

-∞ < x < -4 and 1 < x < ∞

Answer 2

|2x+3|≥0 ——x≥ 3/2

Draw a piecewise function:

2x+3>5 X>-3/2

{

-2x-3>5 X>-3/2

Solve 2x+3>5 when x>-3/2

2x+3>5 = x>1

-2x-3>5 = x<-4

(-∞, -4) U (I,∞)

Thank you!