Solve the System of Inequalities -2x+5<-3x-3 and -4x+9>=-5x+2

$- 2 x + 5 < - 3 x - 3$ and $- 4 x + 9 \geq - 5 x + 2$

Simplify the first inequality.

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

Add $3 x$ to both sides of the inequality.

$- 2 x + 5 + 3 x < - 3$ and $- 4 x + 9 \geq - 5 x + 2$

Add $- 2 x$ and $3 x$ .

$x + 5 < - 3$ and $- 4 x + 9 \geq - 5 x + 2$

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

Subtract $5$ from both sides of the inequality.

$x < - 3 - 5$ and $- 4 x + 9 \geq - 5 x + 2$

Subtract $5$ from $- 3$ .

$x < - 8$ and $- 4 x + 9 \geq - 5 x + 2$

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.

$x < - 8$ and $- 4 x + 9 + 5 x \geq 2$

Add $- 4 x$ and $5 x$ .

$x < - 8$ and $x + 9 \geq 2$

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

Subtract $9$ from both sides of the inequality.

$x < - 8$ and $x \geq 2 - 9$

Subtract $9$ from $2$ .

$x < - 8$ and $x \geq - 7$

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

No solution