Question

Please solve the given problem​

Answer 1

x = -47.1

x = -3.35454... (2-digit repeat)

Explanation:

Each of the absolute value functions causes the overall behavior of the equation to change where that absolute value function's argument is zero. Those values of x are -7, -5/2, -2/5.

These breakpoints cause the domain of the equation to be divided into 4 parts. A graphing calculator shows us that solutions exist only in the two regions ...

• x < -7
• -7 ≤ x < -5/2

In those regions, the equation simplifies to ...

x < -7

2(-(x +2/5)) -2(-(x +7)) = 2/3x +(-(x +5/2))

x(-2 +2) -4/5 +14 = x(2/3 -1) -5/2 . . . . collect terms

15.7 = -1/3x . . . . . . add 5/2

x = -47.1 . . . . . . . multiply by -3

__

-7 ≤ x < -5/2

2(-(x +2/5)) -2(x +7) = 2/3x +(-(x +5/2))

x(-2 -2) -4/5 -14 = x(2/3 -1) -5/2 . . . . collect terms

(-3 2/3)x = 12.3 . . . . . . . . add 1/3x +14.8

x = -36.9/11 = -369/110

x = -3 39/110 ≈ -3.35454... (2-digit repeat)