3|x+9|-4>14 — step-by-step solution

⚠ |x+9| is read as the absolute value abs(x+9)

Let's solve in

ℝ

3 \cdot abs (x + 9) - 4 > 14

3 \cdot abs (x + 9) - 4 - 14 > 0

3 \cdot abs (x + 9) - 18 > 0

This expression can be factorized into:

3 \cdot (abs (x + 9) - 6) > 0

Let's solve:

abs (x + 9) - 6 > 0

abs (A) > B

is equivalent to:

A > B

A < - B

Let's solve in

ℝ

x + 9 > 6

x > 6 - 9

Solution found:

x > -3

Let's solve in

ℝ

x + 9 < -6

x < - 6 - 9

Solution found:

x < -15

▶Solution:

x \in (-∞, -15) \cup (-3, +∞)