Solve 82|7x - 11| ≤ 20

Evaluate

82 ∣ 7 x - 11 ∣ \leq 20

Divide both sides

\frac{82 ∣ 7 x - 11 ∣}{82} \leq \frac{20}{82}

Divide the numbers

∣ 7 x - 11 ∣ \leq \frac{20}{82}

Cancel out the common factor 2

∣ 7 x - 11 ∣ \leq \frac{10}{41}

Separate the inequality into 2 possible cases

{7 x - 11 \leq \frac{10}{41} 7 x - 11 \geq - \frac{10}{41}

Solve the inequality for x

More Steps

{x \leq \frac{461}{287} 7 x - 11 \geq - \frac{10}{41}

Solve the inequality for x

More Steps

{x \leq \frac{461}{287} x \geq \frac{63}{41}

Solution

\frac{63}{41} \leq x \leq \frac{461}{287}

Alternative Form

x \in [\frac{63}{41}, \frac{461}{287}]