Solve the System of Inequalities 2x-11<5x+7<=2x-2

$2 x - 11 < 5 x + 7 \leq 2 x - 2$

Solve $2 x - 11 < 5 x + 7$ for $x$ .

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

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

$2 x - 11 - 5 x < 7$

Subtract $5 x$ from $2 x$ .

$- 3 x - 11 < 7$

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

Add $11$ to both sides of the inequality.

$- 3 x < 7 + 11$

Add $7$ and $11$ .

$- 3 x < 18$

Divide each term in $- 3 x < 18$ by $- 3$ and simplify.

Divide each term in $- 3 x < 18$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} > \frac{18}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} > \frac{18}{- 3}$

Divide $x$ by $1$ .

$x > \frac{18}{- 3}$

Simplify the right side.

Divide $18$ by $- 3$ .

$x > - 6$

Solve $5 x + 7 \leq 2 x - 2$ for $x$ .

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

Subtract $2 x$ from both sides of the inequality.

$5 x + 7 - 2 x \leq - 2$

Subtract $2 x$ from $5 x$ .

$3 x + 7 \leq - 2$

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

Subtract $7$ from both sides of the inequality.

$3 x \leq - 2 - 7$

Subtract $7$ from $- 2$ .

$3 x \leq - 9$

Divide each term in $3 x \leq - 9$ by $3$ and simplify.

Divide each term in $3 x \leq - 9$ by $3$ .

$\frac{3 x}{3} \leq \frac{- 9}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} \leq \frac{- 9}{3}$

Divide $x$ by $1$ .

$x \leq \frac{- 9}{3}$

Simplify the right side.

Divide $- 9$ by $3$ .

$x \leq - 3$

Find the intersection of $x > - 6$ and $x \leq - 3$ .

$- 6 < x \leq - 3$

The result can be shown in multiple forms.

Inequality Form:

$- 6 < x \leq - 3$

Interval Notation:

$(- 6, - 3]$

Solve the System of Inequalities 2x-11<5x+7<=2x-2

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