Solve the System of Inequalities 4x-39>-43 and 8x+31<23

$4 x - 39 > - 43$ and $8 x + 31 < 23$

Simplify the first inequality.

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

Add $39$ to both sides of the inequality.

$4 x > - 43 + 39$ and $8 x + 31 < 23$

Add $- 43$ and $39$ .

$4 x > - 4$ and $8 x + 31 < 23$

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

Divide each term in $4 x > - 4$ by $4$ .

$\frac{4 x}{4} > \frac{- 4}{4}$ and $8 x + 31 < 23$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} > \frac{- 4}{4}$ and $8 x + 31 < 23$

Divide $x$ by $1$ .

$x > \frac{- 4}{4}$ and $8 x + 31 < 23$

Simplify the right side.

Divide $- 4$ by $4$ .

$x > - 1$ and $8 x + 31 < 23$

Simplify the second inequality.

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

Subtract $31$ from both sides of the inequality.

$x > - 1$ and $8 x < 23 - 31$

Subtract $31$ from $23$ .

$x > - 1$ and $8 x < - 8$

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

Divide each term in $8 x < - 8$ by $8$ .

$x > - 1$ and $\frac{8 x}{8} < \frac{- 8}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$x > - 1$ and $\frac{8 x}{8} < \frac{- 8}{8}$

Divide $x$ by $1$ .

$x > - 1$ and $x < \frac{- 8}{8}$

Simplify the right side.

Divide $- 8$ by $8$ .

$x > - 1$ and $x < - 1$

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

No solution