Solve the Inequality for x -4/3x+1/6<7/9

$- \frac{4}{3} x + \frac{1}{6} < \frac{7}{9}$

Simplify each term.

Combine $x$ and $\frac{4}{3}$ .

$- \frac{x \cdot 4}{3} + \frac{1}{6} < \frac{7}{9}$

Move $4$ to the left of $x$ .

$- \frac{4 x}{3} + \frac{1}{6} < \frac{7}{9}$

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

Subtract $\frac{1}{6}$ from both sides of the inequality.

$- \frac{4 x}{3} < \frac{7}{9} - \frac{1}{6}$

To write $\frac{7}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{4 x}{3} < \frac{7}{9} \cdot \frac{2}{2} - \frac{1}{6}$

To write $- \frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{4 x}{3} < \frac{7}{9} \cdot \frac{2}{2} - \frac{1}{6} \cdot \frac{3}{3}$

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{7}{9}$ by $\frac{2}{2}$ .

$- \frac{4 x}{3} < \frac{7 \cdot 2}{9 \cdot 2} - \frac{1}{6} \cdot \frac{3}{3}$

Multiply $9$ by $2$ .

$- \frac{4 x}{3} < \frac{7 \cdot 2}{18} - \frac{1}{6} \cdot \frac{3}{3}$

Multiply $\frac{1}{6}$ by $\frac{3}{3}$ .

$- \frac{4 x}{3} < \frac{7 \cdot 2}{18} - \frac{3}{6 \cdot 3}$

Multiply $6$ by $3$ .

$- \frac{4 x}{3} < \frac{7 \cdot 2}{18} - \frac{3}{18}$

Combine the numerators over the common denominator.

$- \frac{4 x}{3} < \frac{7 \cdot 2 - 3}{18}$

Simplify the numerator.

Multiply $7$ by $2$ .

$- \frac{4 x}{3} < \frac{14 - 3}{18}$

Subtract $3$ from $14$ .

$- \frac{4 x}{3} < \frac{11}{18}$

Divide each term in $- \frac{4 x}{3} < \frac{11}{18}$ by $- 1$ and simplify.

Divide each term in $- \frac{4 x}{3} < \frac{11}{18}$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{4 x}{3}}{- 1} > \frac{\frac{11}{18}}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{4 x}{3}}{1} > \frac{\frac{11}{18}}{- 1}$

Divide $\frac{4 x}{3}$ by $1$ .

$\frac{4 x}{3} > \frac{\frac{11}{18}}{- 1}$

Simplify the right side.

Move the negative one from the denominator of $\frac{\frac{11}{18}}{- 1}$ .

$\frac{4 x}{3} > - 1 \cdot \frac{11}{18}$

Rewrite $- 1 \cdot \frac{11}{18}$ as $- \frac{11}{18}$ .

$\frac{4 x}{3} > - \frac{11}{18}$

Multiply both sides by $3$ .

$\frac{4 x}{3} \cdot 3 > - \frac{11}{18} \cdot 3$

Simplify.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{4 x}{3} \cdot 3 > - \frac{11}{18} \cdot 3$

Rewrite the expression.

$4 x > - \frac{11}{18} \cdot 3$

Simplify the right side.

Simplify $- \frac{11}{18} \cdot 3$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{11}{18}$ into the numerator.

$4 x > \frac{- 11}{18} \cdot 3$

Factor $3$ out of $18$ .

$4 x > \frac{- 11}{3 (6)} \cdot 3$

Cancel the common factor.

$4 x > \frac{- 11}{3 \cdot 6} \cdot 3$

Rewrite the expression.

$4 x > \frac{- 11}{6}$

Move the negative in front of the fraction.

$4 x > - \frac{11}{6}$

Divide each term in $4 x > - \frac{11}{6}$ by $4$ and simplify.

Divide each term in $4 x > - \frac{11}{6}$ by $4$ .

$\frac{4 x}{4} > \frac{- \frac{11}{6}}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} > \frac{- \frac{11}{6}}{4}$

Divide $x$ by $1$ .

$x > \frac{- \frac{11}{6}}{4}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x > - \frac{11}{6} \cdot \frac{1}{4}$

Multiply $- \frac{11}{6} \cdot \frac{1}{4}$ .

Multiply $\frac{1}{4}$ by $\frac{11}{6}$ .

$x > - \frac{11}{4 \cdot 6}$

Multiply $4$ by $6$ .

$x > - \frac{11}{24}$

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{11}{24}$

Interval Notation:

$(- \frac{11}{24}, \infty)$

Solve the Inequality for x -4/3x+1/6<7/9

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