Solve the System of Inequalities 26>3x and -1+2x>=-8

$26 > 3 x$ and $- 1 + 2 x \geq - 8$

Step 1

Simplify the first inequality.

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

$3 x < 26$ and $- 1 + 2 x \geq - 8$

Divide each term in $3 x < 26$ by $3$ and simplify.

Divide each term in $3 x < 26$ by $3$ .

$\frac{3 x}{3} < \frac{26}{3}$ and $- 1 + 2 x \geq - 8$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} < \frac{26}{3}$ and $- 1 + 2 x \geq - 8$

Divide $x$ by $1$ .

$x < \frac{26}{3}$ and $- 1 + 2 x \geq - 8$

Step 2

Simplify the second inequality.

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

Add $1$ to both sides of the inequality.

$x < \frac{26}{3}$ and $2 x \geq - 8 + 1$

Add $- 8$ and $1$ .

$x < \frac{26}{3}$ and $2 x \geq - 7$

Divide each term in $2 x \geq - 7$ by $2$ and simplify.

Divide each term in $2 x \geq - 7$ by $2$ .

$x < \frac{26}{3}$ and $\frac{2 x}{2} \geq \frac{- 7}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$x < \frac{26}{3}$ and $\frac{2 x}{2} \geq \frac{- 7}{2}$

Divide $x$ by $1$ .

$x < \frac{26}{3}$ and $x \geq \frac{- 7}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x < \frac{26}{3}$ and $x \geq - \frac{7}{2}$

Step 3

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

$- \frac{7}{2} \leq x < \frac{26}{3}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- \frac{7}{2} \leq x < \frac{26}{3}$

Interval Notation:

$[- \frac{7}{2}, \frac{26}{3})$

Step 5