Question

The inequality 7 - 2/3x < x - 8 is equivalent to

a. x > 9

b. x > -3/5

c. x < 9

d. x < -3/5

please show work

Answer 1

a. x > 9

Explanation:

7 - 2/3x < x - 8

Add 2/3 x to each side

7 - 2/3x+ 2/3 x < x+ 2/3 x - 8

7 < x + 2/3 x -8

Add 8 to each side

7+8 < x + 2/3 x -8+8

15 < x + 2/3 x

Get a common denominator for x of 3

15 < 3/3 x + 2/3 x

15 < 5/3 x

Multiply by 3/5 to isolate x

3/5 * 15 < 5/3x * 3/5

9 < x