Solve the System of Inequalities 3x+1<5x+7 and -2x+5<=-5x-10

$3 x + 1 < 5 x + 7$ and $- 2 x + 5 \leq - 5 x - 10$

Step 1

Simplify the first inequality.

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

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

$3 x + 1 - 5 x < 7$ and $- 2 x + 5 \leq - 5 x - 10$

Subtract $5 x$ from $3 x$ .

$- 2 x + 1 < 7$ and $- 2 x + 5 \leq - 5 x - 10$

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

Subtract $1$ from both sides of the inequality.

$- 2 x < 7 - 1$ and $- 2 x + 5 \leq - 5 x - 10$

Subtract $1$ from $7$ .

$- 2 x < 6$ and $- 2 x + 5 \leq - 5 x - 10$

Divide each term in $- 2 x < 6$ by $- 2$ and simplify.

Divide each term in $- 2 x < 6$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} > \frac{6}{- 2}$ and $- 2 x + 5 \leq - 5 x - 10$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} > \frac{6}{- 2}$ and $- 2 x + 5 \leq - 5 x - 10$

Divide $x$ by $1$ .

$x > \frac{6}{- 2}$ and $- 2 x + 5 \leq - 5 x - 10$

Simplify the right side.

Divide $6$ by $- 2$ .

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

Step 2

Simplify the second inequality.

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

Add $5 x$ to both sides of the inequality.

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

Add $- 2 x$ and $5 x$ .

$x > - 3$ and $3 x + 5 \leq - 10$

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

Subtract $5$ from both sides of the inequality.

$x > - 3$ and $3 x \leq - 10 - 5$

Subtract $5$ from $- 10$ .

$x > - 3$ and $3 x \leq - 15$

Divide each term in $3 x \leq - 15$ by $3$ and simplify.

Divide each term in $3 x \leq - 15$ by $3$ .

$x > - 3$ and $\frac{3 x}{3} \leq \frac{- 15}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$x > - 3$ and $\frac{3 x}{3} \leq \frac{- 15}{3}$

Divide $x$ by $1$ .

$x > - 3$ and $x \leq \frac{- 15}{3}$

Simplify the right side.

Divide $- 15$ by $3$ .

$x > - 3$ and $x \leq - 5$

Step 3

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

No solution

Solve the System of Inequalities 3x+1<5x+7 and -2x+5<=-5x-10

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