|7x+1/2 |-2<8 — step-by-step solution

1) Let's solve in

ℝ

| 7 x + \frac{1}{2} | - 2 < 8

ⓘ We add

2

to both sides

| 7 x + \frac{1}{2} | < 8 + 2

ⓘ Start from

8

and move forward

2

on the number line:

8 + 2

10

| 7 x + \frac{1}{2} | < 10

| A | < B

is equivalent to

- B < A < B

-10 < 7 x + \frac{1}{2} < 10

We add

- \frac{1}{2}

to all three parts of the inequality

- \frac{21}{2} < 7 x < \frac{19}{2}

We divide all three parts by

7

, which is positive

- \frac{3}{2} < x < \frac{19}{14}

▶Solution found:

x \in (- \frac{3}{2}, \frac{19}{14})

2) The numeric value of:

x \in (- \frac{3}{2}, \frac{19}{14})

equals:

▷

x \in (-1.5, \approx 1.3571)