|(x-3)/4 |>5 — step-by-step solution

1) Let's solve in

ℝ

| \frac{x - 3}{4} | > 5

| A | > B

is equivalent to:

A > B

A < - B

2) Let's solve in

ℝ

\frac{x - 3}{4} > 5

x - 3 > 5 \cdot 4

ⅰ

5 \cdot 4

20

x - 3 > 20

ⓘ We add

3

to both sides

x > 20 + 3

ⓘ Start from

20

and move forward

3

on the number line:

20 + 3

23

Solution found:

x > 23

3) Let's solve in

ℝ

\frac{x - 3}{4} < -5

x - 3 < -5 \cdot 4

ⓘ A single minus sign does not cancel out, the product of a negative number by a positive number is negative:

-5 \cdot 4

-20

x - 3 < -20

ⓘ We add

3

to both sides

x < - 20 + 3

ⓘ Start from

-20

and move forward

3

on the number line, getting closer to zero:

- 20 + 3

-17

Solution obtained:

x < -17

▶Solution:

x \in (-∞, -17) \cup (23, +∞)