|(x+1)/2 |>4 — step-by-step solution | Explain MAths

|(x+1)/2 |>4

1) Let's solve in

ℝ

:

| \frac{x + 1}{2} | > 4

| A | > B

is equivalent to:

A > B

or

A < - B

2) Let's solve in

ℝ

:

\frac{x + 1}{2} > 4

x + 1 > 4 \cdot 2

ⅰ

4 \cdot 2

=

8

x + 1 > 8

ⓘ We subtract

1

from both sides

x > 8 - 1

ⓘ Start from

8

and move back

1

on the number line:

8 - 1

=

7

Solution found:

x > 7

3) Let's solve in

ℝ

:

\frac{x + 1}{2} < -4

x + 1 < -4 \cdot 2

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

-4 \cdot 2

=

-8

x + 1 < -8

ⓘ We subtract

1

from both sides

x < - 8 - 1

ⓘ Start from

-8

and move back

1

more on the number line, away from zero:

- 8 - 1

=

-9

Solution found:

x < -9

▶Solution:

x \in (-∞, -9) \cup (7, +∞)