-8+6|-3x+3|>82 — step-by-step solution

1) Let's solve in

ℝ

- 8 + 6 \cdot | - 3 x + 3 | > 82

ⓘ We add

8

to both sides

6 \cdot | - 3 x + 3 | > 82 + 8

ⓘ Start from

82

and move forward

8

on the number line:

82 + 8

90

6 \cdot | - 3 x + 3 | > 90

Since

6 > 0

, divide both sides by

6

without reversing the inequality:

| - 3 x + 3 | > 15

| A | > B

is equivalent to:

A > B

A < - B

2) Let's solve in

ℝ

- 3 x + 3 > 15

ⓘ We gather the terms in

x

on the right and the other terms on the left

3 - 15 > 3 x

ⓘ Start from

3

and move back

15

on the number line, going below zero:

3 - 15

-12

-12 > 3 x

ⓘ Both sides are divided by

3

x < - \frac{12}{3}

ⓘ We simplify the fraction by dividing the numerator and the denominator by

3

, their greatest common divisor:

- \frac{12}{3}

-4

Solution found:

x < -4

3) Let's solve in

ℝ

- 3 x + 3 < -15

ⓘ We gather the terms in

x

on the right and the other terms on the left

3 + 15 < 3 x

ⓘ Start from

3

and move forward

15

on the number line:

3 + 15

18

18 < 3 x

ⓘ Both sides are divided by

3

x > \frac{18}{3}

ⓘ We simplify the fraction by dividing the numerator and the denominator by

3

, their greatest common divisor:

\frac{18}{3}

6

Solution found:

x > 6

▶Solution:

x \in (-∞, -4) \cup (6, +∞)