| 7/8 x-10|<14 — step-by-step solution

⚠Ⓘ 7/8 x-10|<14 is read as (7/8)*x-10|<14: use parentheses around the denominator to include the following factor in it

1) Let's solve in

ℝ

| \frac{7}{8} \cdot x - 10 | < 14

| \frac{7 x}{8} - 10 | < 14

abs (A) < B

means that:

A < B

and

A > - B

2) Let's solve in

ℝ

\frac{7 x}{8} - 10 < 14

\frac{7 x}{8} < 14 + 10

\frac{7 x}{8} < 24

7 x < 8 \cdot 24

x < \frac{8 \cdot 24}{7}

Solution found:

x < \frac{192}{7}

3) Let's solve in

ℝ

\frac{7 x}{8} - 10 > -14

\frac{7 x}{8} > - 14 + 10

\frac{7 x}{8} > -4

7 x > 8 \cdot (-4)

x > \frac{8 \cdot (-4)}{7}

Solution found:

x > - \frac{32}{7}

Let's create the table of the different solutions to find the overall solution:

▶Solution obtained:

x \in (- \frac{32}{7}, \frac{192}{7})

4) The numeric value of:

x \in (- \frac{32}{7}, \frac{192}{7})

equals:

▷

x \in (\approx -4.5714, \approx 27.4286)