Solve the System of Inequalities 8x<24 and -8<=2x-4

$8 x < 24$ and $- 8 \leq 2 x - 4$

Step 1

Divide each term in $8 x < 24$ by $8$ and simplify.

Divide each term in $8 x < 24$ by $8$ .

$\frac{8 x}{8} < \frac{24}{8}$ and $- 8 \leq 2 x - 4$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} < \frac{24}{8}$ and $- 8 \leq 2 x - 4$

Divide $x$ by $1$ .

$x < \frac{24}{8}$ and $- 8 \leq 2 x - 4$

Simplify the right side.

Divide $24$ by $8$ .

$x < 3$ and $- 8 \leq 2 x - 4$

Step 2

Simplify the second inequality.

Rewrite so $x$ is on the left side of the inequality.

$x < 3$ and $2 x - 4 \geq - 8$

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

Add $4$ to both sides of the inequality.

$x < 3$ and $2 x \geq - 8 + 4$

Add $- 8$ and $4$ .

$x < 3$ and $2 x \geq - 4$

Divide each term in $2 x \geq - 4$ by $2$ and simplify.

Divide each term in $2 x \geq - 4$ by $2$ .

$x < 3$ and $\frac{2 x}{2} \geq \frac{- 4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$x < 3$ and $\frac{2 x}{2} \geq \frac{- 4}{2}$

Divide $x$ by $1$ .

$x < 3$ and $x \geq \frac{- 4}{2}$

Simplify the right side.

Divide $- 4$ by $2$ .

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

Step 3

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

$- 2 \leq x < 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 2 \leq x < 3$

Interval Notation:

$[- 2, 3)$

Step 5