Convert to Interval Notation 5x-7<=7x-11<=5x+9

$5 x - 7 \leq 7 x - 11 \leq 5 x + 9$

Step 1

Move all terms not containing $x$ from the center section of the inequality.

Add $11$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$5 x - 7 + 11 \leq 7 x \leq 5 x + 9 + 11$

Add $- 7$ and $11$ .

$5 x + 4 \leq 7 x \leq 5 x + 9 + 11$

Add $9$ and $11$ .

$5 x + 4 \leq 7 x \leq 5 x + 20$

Step 2

Divide each term in the inequality by $7$ .

$\frac{5 x}{7} + \frac{4}{7} \leq \frac{7 x}{7} \leq \frac{5 x}{7} + \frac{20}{7}$

Step 3

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{5 x}{7} + \frac{4}{7} \leq \frac{7 x}{7} \leq \frac{5 x}{7} + \frac{20}{7}$

Divide $x$ by $1$ .

$\frac{5 x}{7} + \frac{4}{7} \leq x \leq \frac{5 x}{7} + \frac{20}{7}$

Step 4

Convert the inequality to interval notation.

$[\frac{5 x}{7} + \frac{4}{7}, \frac{5 x}{7} + \frac{20}{7}]$

Step 5