|1-7x|+2>= 4 — step-by-step solution | Explain MAths

|1-7x|+2>= 4

1) Let's solve in

ℝ

:

| 1 - 7 x | + 2 \geq 4

ⓘ We subtract

2

from both sides

| 1 - 7 x | \geq 4 - 2

ⓘ Start from

4

and move back

2

on the number line:

4 - 2

=

2

| 1 - 7 x | \geq 2

| A | \geq B

means that:

A \geq B

or

A \leq - B

2) Let's solve in

ℝ

:

1 - 7 x \geq 2

ⓘ We gather the terms in

x

on the right and the other terms on the left

1 - 2 \geq 7 x

ⓘ Start from

1

and move back

2

on the number line, going below zero:

1 - 2

=

-1

-1 \geq 7 x

ⓘ Both sides are divided by

7

Solution obtained:

x \leq - \frac{1}{7}

3) Let's solve in

ℝ

:

1 - 7 x \leq -2

ⓘ We gather the terms in

x

on the right and the other terms on the left

1 + 2 \leq 7 x

ⓘ Start from

1

and move forward

2

on the number line:

1 + 2

=

3

3 \leq 7 x

ⓘ Both sides are divided by

7

Solution obtained:

x \geq \frac{3}{7}

▶Solution:

x \in (-∞, - \frac{1}{7}] \cup [\frac{3}{7}, +∞)

4) The numeric value of:

x \in (-∞, - \frac{1}{7}] \cup [\frac{3}{7}, +∞)

equals:

▷

x \in (-∞, \approx -0.1429] \cup [\approx 0.4286, +∞)