Solve the Inequality for x 5x+2<x-3<4x-5

$5 x + 2 < x - 3 < 4 x - 5$

Solve $5 x + 2 < x - 3$ for $x$ .

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

Subtract $x$ from both sides of the inequality.

$5 x + 2 - x < - 3$

Subtract $x$ from $5 x$ .

$4 x + 2 < - 3$

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

Subtract $2$ from both sides of the inequality.

$4 x < - 3 - 2$

Subtract $2$ from $- 3$ .

$4 x < - 5$

Divide each term in $4 x < - 5$ by $4$ and simplify.

Divide each term in $4 x < - 5$ by $4$ .

$\frac{4 x}{4} < \frac{- 5}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} < \frac{- 5}{4}$

Divide $x$ by $1$ .

$x < \frac{- 5}{4}$

Simplify the right side.

Move the negative in front of the fraction.

$x < - \frac{5}{4}$

Solve $x - 3 < 4 x - 5$ for $x$ .

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

Subtract $4 x$ from both sides of the inequality.

$x - 3 - 4 x < - 5$

Subtract $4 x$ from $x$ .

$- 3 x - 3 < - 5$

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

Add $3$ to both sides of the inequality.

$- 3 x < - 5 + 3$

Add $- 5$ and $3$ .

$- 3 x < - 2$

Divide each term in $- 3 x < - 2$ by $- 3$ and simplify.

Divide each term in $- 3 x < - 2$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} > \frac{- 2}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} > \frac{- 2}{- 3}$

Divide $x$ by $1$ .

$x > \frac{- 2}{- 3}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x > \frac{2}{3}$

Find the intersection of $x < - \frac{5}{4}$ and $x > \frac{2}{3}$ .

No solution

Solve the Inequality for x 5x+2<x-3<4x-5

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