Solve the System of Inequalities -3x-1<=2x+9 and -4x+3>-2x+11

$- 3 x - 1 \leq 2 x + 9$ and $- 4 x + 3 > - 2 x + 11$

Step 1

Simplify the first inequality.

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

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

$- 3 x - 1 - 2 x \leq 9$ and $- 4 x + 3 > - 2 x + 11$

Subtract $2 x$ from $- 3 x$ .

$- 5 x - 1 \leq 9$ and $- 4 x + 3 > - 2 x + 11$

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

Add $1$ to both sides of the inequality.

$- 5 x \leq 9 + 1$ and $- 4 x + 3 > - 2 x + 11$

Add $9$ and $1$ .

$- 5 x \leq 10$ and $- 4 x + 3 > - 2 x + 11$

Divide each term in $- 5 x \leq 10$ by $- 5$ and simplify.

Divide each term in $- 5 x \leq 10$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 x}{- 5} \geq \frac{10}{- 5}$ and $- 4 x + 3 > - 2 x + 11$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} \geq \frac{10}{- 5}$ and $- 4 x + 3 > - 2 x + 11$

Divide $x$ by $1$ .

$x \geq \frac{10}{- 5}$ and $- 4 x + 3 > - 2 x + 11$

Simplify the right side.

Divide $10$ by $- 5$ .

$x \geq - 2$ and $- 4 x + 3 > - 2 x + 11$

Step 2

Simplify the second inequality.

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

Add $2 x$ to both sides of the inequality.

$x \geq - 2$ and $- 4 x + 3 + 2 x > 11$

Add $- 4 x$ and $2 x$ .

$x \geq - 2$ and $- 2 x + 3 > 11$

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

Subtract $3$ from both sides of the inequality.

$x \geq - 2$ and $- 2 x > 11 - 3$

Subtract $3$ from $11$ .

$x \geq - 2$ and $- 2 x > 8$

Divide each term in $- 2 x > 8$ by $- 2$ and simplify.

Divide each term in $- 2 x > 8$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$x \geq - 2$ and $\frac{- 2 x}{- 2} < \frac{8}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$x \geq - 2$ and $\frac{- 2 x}{- 2} < \frac{8}{- 2}$

Divide $x$ by $1$ .

$x \geq - 2$ and $x < \frac{8}{- 2}$

Simplify the right side.

Divide $8$ by $- 2$ .

$x \geq - 2$ and $x < - 4$

Step 3

The intersection consists of the elements that are contained in both intervals.

No solution

Solve the System of Inequalities -3x-1<=2x+9 and -4x+3>-2x+11

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