Solve 5-8|7x-5|≤1

Evaluate

5 - 8 ∣ 7 x - 5 ∣ \leq 1

Move the expression to the left side

5 - 8 ∣ 7 x - 5 ∣ - 1 \leq 0

Subtract the numbers

4 - 8 ∣ 7 x - 5 ∣ \leq 0

Rewrite the expression

- 8 ∣ 7 x - 5 ∣ \leq - 4

Change the signs on both sides of the inequality and flip the inequality sign

8 ∣ 7 x - 5 ∣ \geq 4

Divide both sides

\frac{8 ∣ 7 x - 5 ∣}{8} \geq \frac{4}{8}

Divide the numbers

∣ 7 x - 5 ∣ \geq \frac{4}{8}

Cancel out the common factor 4

∣ 7 x - 5 ∣ \geq \frac{1}{2}

Separate the inequality into 2 possible cases

7 x - 5 \geq \frac{1}{2} 7 x - 5 \leq - \frac{1}{2}

Solve the inequality for x

More Steps

x \geq \frac{11}{14} 7 x - 5 \leq - \frac{1}{2}

Solve the inequality for x

More Steps

x \geq \frac{11}{14} x \leq \frac{9}{14}

Solution

x \in (- \infty, \frac{9}{14}] \cup [\frac{11}{14}, + \infty)