Solve the Inequality for x 5x-7<=7x-11<=5x+9

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

Solve $5 x - 7 \leq 7 x - 11$ for $x$ .

Move all terms containing $x$ to the left side of the inequality.

Subtract $7 x$ from both sides of the inequality.

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

Subtract $7 x$ from $5 x$ .

$- 2 x - 7 \leq - 11$

Move all terms not containing $x$ to the right side of the inequality.

Add $7$ to both sides of the inequality.

$- 2 x \leq - 11 + 7$

Add $- 11$ and $7$ .

$- 2 x \leq - 4$

Divide each term in $- 2 x \leq - 4$ by $- 2$ and simplify.

Divide each term in $- 2 x \leq - 4$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} \geq \frac{- 4}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} \geq \frac{- 4}{- 2}$

Divide $x$ by $1$ .

$x \geq \frac{- 4}{- 2}$

Simplify the right side.

Divide $- 4$ by $- 2$ .

$x \geq 2$

Solve $7 x - 11 \leq 5 x + 9$ for $x$ .

Move all terms containing $x$ to the left side of the inequality.

Subtract $5 x$ from both sides of the inequality.

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

Subtract $5 x$ from $7 x$ .

$2 x - 11 \leq 9$

Move all terms not containing $x$ to the right side of the inequality.

Add $11$ to both sides of the inequality.

$2 x \leq 9 + 11$

Add $9$ and $11$ .

$2 x \leq 20$

Divide each term in $2 x \leq 20$ by $2$ and simplify.

Divide each term in $2 x \leq 20$ by $2$ .

$\frac{2 x}{2} \leq \frac{20}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \leq \frac{20}{2}$

Divide $x$ by $1$ .

$x \leq \frac{20}{2}$

Simplify the right side.

Divide $20$ by $2$ .

$x \leq 10$

Find the intersection of $x \geq 2$ and $x \leq 10$ .

$2 \leq x \leq 10$

The result can be shown in multiple forms.

Inequality Form:

$2 \leq x \leq 10$

Interval Notation:

$[2, 10]$

Solve the Inequality for x 5x-7<=7x-11<=5x+9

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