|7x-5|+3>= 9 — step-by-step solution | Explain MAths

|7x-5|+3>= 9

1) Let's solve in

ℝ

:

| 7 x - 5 | + 3 \geq 9

ⓘ We subtract

3

from both sides

| 7 x - 5 | \geq 9 - 3

ⓘ Start from

9

and move back

3

on the number line:

9 - 3

=

6

| 7 x - 5 | \geq 6

| A | \geq B

means that:

A \geq B

or

A \leq - B

2) Let's solve in

ℝ

:

7 x - 5 \geq 6

ⓘ We add

5

to both sides

7 x \geq 6 + 5

ⓘ Start from

6

and move forward

5

on the number line:

6 + 5

=

11

7 x \geq 11

ⓘ Both sides are divided by

7

Solution found:

x \geq \frac{11}{7}

3) Let's solve in

ℝ

:

7 x - 5 \leq -6

ⓘ We add

5

to both sides

7 x \leq - 6 + 5

ⓘ Start from

-6

and move forward

5

on the number line, getting closer to zero:

- 6 + 5

=

-1

7 x \leq -1

ⓘ Both sides are divided by

7

Solution obtained:

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

▶Solution:

x \in (-∞, - \frac{1}{7}] \cup [\frac{11}{7}, +∞)

4) The numeric value of:

x \in (-∞, - \frac{1}{7}] \cup [\frac{11}{7}, +∞)

equals:

▷

x \in (-∞, \approx -0.1429] \cup [\approx 1.5714, +∞)