Convert to Interval Notation 5-2x>31 and 7x+8>=-55

$5 - 2 x > 31$ and $7 x + 8 \geq - 55$

Step 1

Simplify the first inequality.

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

Subtract $5$ from both sides of the inequality.

$- 2 x > 31 - 5$ and $7 x + 8 \geq - 55$

Subtract $5$ from $31$ .

$- 2 x > 26$ and $7 x + 8 \geq - 55$

Divide each term in $- 2 x > 26$ by $- 2$ and simplify.

Divide each term in $- 2 x > 26$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} < \frac{26}{- 2}$ and $7 x + 8 \geq - 55$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} < \frac{26}{- 2}$ and $7 x + 8 \geq - 55$

Divide $x$ by $1$ .

$x < \frac{26}{- 2}$ and $7 x + 8 \geq - 55$

Simplify the right side.

Divide $26$ by $- 2$ .

$x < - 13$ and $7 x + 8 \geq - 55$

Step 2

Simplify the second inequality.

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

Subtract $8$ from both sides of the inequality.

$x < - 13$ and $7 x \geq - 55 - 8$

Subtract $8$ from $- 55$ .

$x < - 13$ and $7 x \geq - 63$

Divide each term in $7 x \geq - 63$ by $7$ and simplify.

Divide each term in $7 x \geq - 63$ by $7$ .

$x < - 13$ and $\frac{7 x}{7} \geq \frac{- 63}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$x < - 13$ and $\frac{7 x}{7} \geq \frac{- 63}{7}$

Divide $x$ by $1$ .

$x < - 13$ and $x \geq \frac{- 63}{7}$

Simplify the right side.

Divide $- 63$ by $7$ .

$x < - 13$ and $x \geq - 9$

Step 3

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

No solution

Convert to Interval Notation 5-2x>31 and 7x+8>=-55

Related Questions

Support LCMGCF.com by disabling your adblocker.