Find the Intersection of the Inequalities 6x-21>=-3 , 14x+11<-17

$6 x - 21 \geq - 3$ , $14 x + 11 < - 17$

Step 1

Simplify the first inequality.

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

Add $21$ to both sides of the inequality.

$6 x \geq - 3 + 21$ and $14 x + 11 < - 17$

Add $- 3$ and $21$ .

$6 x \geq 18$ and $14 x + 11 < - 17$

Divide each term in $6 x \geq 18$ by $6$ and simplify.

Divide each term in $6 x \geq 18$ by $6$ .

$\frac{6 x}{6} \geq \frac{18}{6}$ and $14 x + 11 < - 17$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} \geq \frac{18}{6}$ and $14 x + 11 < - 17$

Divide $x$ by $1$ .

$x \geq \frac{18}{6}$ and $14 x + 11 < - 17$

Simplify the right side.

Divide $18$ by $6$ .

$x \geq 3$ and $14 x + 11 < - 17$

Step 2

Simplify the second inequality.

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

Subtract $11$ from both sides of the inequality.

$x \geq 3$ and $14 x < - 17 - 11$

Subtract $11$ from $- 17$ .

$x \geq 3$ and $14 x < - 28$

Divide each term in $14 x < - 28$ by $14$ and simplify.

Divide each term in $14 x < - 28$ by $14$ .

$x \geq 3$ and $\frac{14 x}{14} < \frac{- 28}{14}$

Simplify the left side.

Cancel the common factor of $14$ .

Cancel the common factor.

$x \geq 3$ and $\frac{14 x}{14} < \frac{- 28}{14}$

Divide $x$ by $1$ .

$x \geq 3$ and $x < \frac{- 28}{14}$

Simplify the right side.

Divide $- 28$ by $14$ .

$x \geq 3$ and $x < - 2$

Step 3

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

No solution