Solve for x 0>x-7/3>-3

$0 > x - \frac{7}{3} > - 3$

Step 1

Move all terms not containing $x$ from the center section of the inequality.

Add $\frac{7}{3}$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$0 + \frac{7}{3} > x > - 3 + \frac{7}{3}$

Add $0$ and $\frac{7}{3}$ .

$\frac{7}{3} > x > - 3 + \frac{7}{3}$

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{7}{3} > x > - 3 \cdot \frac{3}{3} + \frac{7}{3}$

Combine $- 3$ and $\frac{3}{3}$ .

$\frac{7}{3} > x > \frac{- 3 \cdot 3}{3} + \frac{7}{3}$

Combine the numerators over the common denominator.

$\frac{7}{3} > x > \frac{- 3 \cdot 3 + 7}{3}$

Simplify the numerator.

Multiply $- 3$ by $3$ .

$\frac{7}{3} > x > \frac{- 9 + 7}{3}$

Add $- 9$ and $7$ .

$\frac{7}{3} > x > \frac{- 2}{3}$

Move the negative in front of the fraction.

$\frac{7}{3} > x > - \frac{2}{3}$

Step 2

Rewrite the interval so that the left value is less than the right value. This is the correct way to write an interval solution.

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

Step 3

The result can be shown in multiple forms.

Inequality Form:

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

Interval Notation:

$(- \frac{2}{3}, \frac{7}{3})$

Step 4