Question

Solve the absolute value inequality: |2x - 3| < 7
Answer x > -2 and x < 5

x < -2 or x > 5
x > -2 or x < 5
x < -2 and x > 5

Answer 1

=> -7<2x-3<7
=> -7+3<2x-3+3<7+3
=> -4 < 2x < 10
=> -2 < x < 5
i.e x> -2 and x<5

Answer 2

first way to solve it since we have the absolute value thingies:

2x-3 <7
-add 3 to both sides, which leaves you with
2x < 10
-divide by 2, which leaves you with
x < 5

second way to solve it:

-2x+3 <7
-subtract 3, which leaves you with
-2x < 4
- divide by 2, make sure to switch your sign b/c your dividing with a negative, which leaves you with
x > -2

so your answer is x > -2 and x < 5.

Answer 3

Do you understand how the absolute value thing works?