Solve the Inequality for x 3x+1<2x-2<5x+7

$3 x + 1 < 2 x - 2 < 5 x + 7$

Step 1

Solve $3 x + 1 < 2 x - 2$ for $x$ .

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

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

$3 x + 1 - 2 x < - 2$

Subtract $2 x$ from $3 x$ .

$x + 1 < - 2$

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

Subtract $1$ from both sides of the inequality.

$x < - 2 - 1$

Subtract $1$ from $- 2$ .

$x < - 3$

Step 2

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

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

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

$2 x - 2 - 5 x < 7$

Subtract $5 x$ from $2 x$ .

$- 3 x - 2 < 7$

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

Add $2$ to both sides of the inequality.

$- 3 x < 7 + 2$

Add $7$ and $2$ .

$- 3 x < 9$

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

Divide each term in $- 3 x < 9$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $9$ by $- 3$ .

$x > - 3$

Step 3

Find the intersection of $x < - 3$ and $x > - 3$ .

No solution

Solve the Inequality for x 3x+1<2x-2<5x+7

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