Solve for x 7-2/3x<x-8

$7 - \frac{2}{3} x < x - 8$

Step 1

Simplify each term.

Combine $x$ and $\frac{2}{3}$ .

$7 - \frac{x \cdot 2}{3} < x - 8$

Move $2$ to the left of $x$ .

$7 - \frac{2 x}{3} < x - 8$

Step 2

Move all terms containing $x$ to the left side of the inequality.

Subtract $x$ from both sides of the inequality.

$7 - \frac{2 x}{3} - x < - 8$

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

$7 - \frac{2 x}{3} - x \cdot \frac{3}{3} < - 8$

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

$7 - \frac{2 x}{3} + \frac{- x \cdot 3}{3} < - 8$

Combine the numerators over the common denominator.

$7 + \frac{- 2 x - x \cdot 3}{3} < - 8$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- 2 x - x \cdot 3$ .

Factor $x$ out of $- 2 x$ .

$7 + \frac{x \cdot - 2 - x \cdot 3}{3} < - 8$

Factor $x$ out of $- x \cdot 3$ .

$7 + \frac{x \cdot - 2 + x (- 1 \cdot 3)}{3} < - 8$

Factor $x$ out of $x \cdot - 2 + x (- 1 \cdot 3)$ .

$7 + \frac{x (- 2 - 1 \cdot 3)}{3} < - 8$

Multiply $- 1$ by $3$ .

$7 + \frac{x (- 2 - 3)}{3} < - 8$

Subtract $3$ from $- 2$ .

$7 + \frac{x \cdot - 5}{3} < - 8$

Move $- 5$ to the left of $x$ .

$7 + \frac{- 5 \cdot x}{3} < - 8$

Move the negative in front of the fraction.

$7 - \frac{5 x}{3} < - 8$

Step 3

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

Subtract $7$ from both sides of the inequality.

$- \frac{5 x}{3} < - 8 - 7$

Subtract $7$ from $- 8$ .

$- \frac{5 x}{3} < - 15$

Step 4

Divide each term in $- \frac{5 x}{3} < - 15$ by $- 1$ and simplify.

Divide each term in $- \frac{5 x}{3} < - 15$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{5 x}{3}}{- 1} > \frac{- 15}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{5 x}{3}}{1} > \frac{- 15}{- 1}$

Divide $\frac{5 x}{3}$ by $1$ .

$\frac{5 x}{3} > \frac{- 15}{- 1}$

Simplify the right side.

Divide $- 15$ by $- 1$ .

$\frac{5 x}{3} > 15$

Step 5

Multiply both sides by $3$ .

$\frac{5 x}{3} \cdot 3 > 15 \cdot 3$

Step 6

Simplify.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{5 x}{3} \cdot 3 > 15 \cdot 3$

Rewrite the expression.

$5 x > 15 \cdot 3$

Simplify the right side.

Multiply $15$ by $3$ .

$5 x > 45$

Step 7

Divide each term in $5 x > 45$ by $5$ and simplify.

Divide each term in $5 x > 45$ by $5$ .

$\frac{5 x}{5} > \frac{45}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} > \frac{45}{5}$

Divide $x$ by $1$ .

$x > \frac{45}{5}$

Simplify the right side.

Divide $45$ by $5$ .

$x > 9$

Step 8

The result can be shown in multiple forms.

Inequality Form:

$x > 9$

Interval Notation:

$(9, \infty)$

Solve for x 7-2/3x<x-8

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