2|v-7|-4>= 42 — step-by-step solution | Explain MAths

2|v-7|-4>= 42

1) Let's solve in

ℝ

:

2 \cdot | v - 7 | - 4 \geq 42

ⓘ We add

4

to both sides

2 \cdot | v - 7 | \geq 42 + 4

ⓘ Start from

42

and move forward

4

on the number line:

42 + 4

=

46

2 \cdot | v - 7 | \geq 46

Since

2 > 0

, divide both sides by

2

without reversing the inequality:

| v - 7 | \geq 23

| A | \geq B

means that:

A \geq B

or

A \leq - B

2) Let's solve in

ℝ

:

v - 7 \geq 23

ⓘ We add

7

to both sides

v \geq 23 + 7

ⓘ Start from

23

and move forward

7

on the number line:

23 + 7

=

30

Solution obtained:

v \geq 30

3) Let's solve in

ℝ

:

v - 7 \leq -23

ⓘ We add

7

to both sides

v \leq - 23 + 7

ⓘ Start from

-23

and move forward

7

on the number line, getting closer to zero:

- 23 + 7

=

-16

Solution found:

v \leq -16

▶Solution:

v \in (-∞, -16] \cup [30, +∞)