-5x + 8 ? 3x + 8 (please explain solving this)

Question

-5x + 8 ? 3x + 8 (please explain solving this)

X

Answer 1

Solving inequality is very like solving equation. The only difference: if divide or multiply both sides of inequality by negative number, we have to change sign of inequality to opposite.
~~~~~~~~~~

-5x + 8  ≥  3x + 8
       - 8           - 8

- 5x   ≥   3x
- 3x      - 3x

   - 8x   ≥    0
÷(- 8)    ÷(- 8)

    x ≤ 0  ,  or all real numbers out of interval (- ∞, 0]

 <====|=====•———|————>

- ∞    - 10         0       10       + ∞


Let's verify the answer:

for x = -10,

-5 × (-10) + 8 ≥ 3 × (- 10) + 8
           50 + 8 ≥ -30 + 8
                 42 ≥ - 22    (True)

for x = 10,

- 5 × 10 + 8 ≥ 3 × 10 + 8
      - 50 + 8 ≥ 30 + 8
            - 42 ≥ 38     (False)

Answer 2

Are you setting them equal? or is it an inequality?   there needs to be a sign where the ? is to know what exactly you're trying to find.