Solve the Inequality for x 2/3x+14-3x>-7

$\frac{2}{3} x + 14 - 3 x > - 7$

Simplify $\frac{2}{3} x + 14 - 3 x$ .

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

$\frac{2 x}{3} + 14 - 3 x > - 7$

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

$\frac{2 x}{3} - 3 x \cdot \frac{3}{3} + 14 > - 7$

Simplify terms.

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

$\frac{2 x}{3} + \frac{- 3 x \cdot 3}{3} + 14 > - 7$

Combine the numerators over the common denominator.

$\frac{2 x - 3 x \cdot 3}{3} + 14 > - 7$

Simplify each term.

Simplify the numerator.

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

Factor $x$ out of $2 x$ .

$\frac{x \cdot 2 - 3 x \cdot 3}{3} + 14 > - 7$

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

$\frac{x \cdot 2 + x (- 3 \cdot 3)}{3} + 14 > - 7$

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

$\frac{x (2 - 3 \cdot 3)}{3} + 14 > - 7$

Multiply $- 3$ by $3$ .

$\frac{x (2 - 9)}{3} + 14 > - 7$

Subtract $9$ from $2$ .

$\frac{x \cdot - 7}{3} + 14 > - 7$

Move $- 7$ to the left of $x$ .

$\frac{- 7 \cdot x}{3} + 14 > - 7$

Move the negative in front of the fraction.

$- \frac{7 x}{3} + 14 > - 7$

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

Subtract $14$ from both sides of the inequality.

$- \frac{7 x}{3} > - 7 - 14$

Subtract $14$ from $- 7$ .

$- \frac{7 x}{3} > - 21$

Divide each term in $- \frac{7 x}{3} > - 21$ by $- 1$ and simplify.

Divide each term in $- \frac{7 x}{3} > - 21$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{7 x}{3}}{- 1} < \frac{- 21}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{7 x}{3}}{1} < \frac{- 21}{- 1}$

Divide $\frac{7 x}{3}$ by $1$ .

$\frac{7 x}{3} < \frac{- 21}{- 1}$

Simplify the right side.

Divide $- 21$ by $- 1$ .

$\frac{7 x}{3} < 21$

Multiply both sides by $3$ .

$\frac{7 x}{3} \cdot 3 < 21 \cdot 3$

Simplify.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{7 x}{3} \cdot 3 < 21 \cdot 3$

Rewrite the expression.

$7 x < 21 \cdot 3$

Simplify the right side.

Multiply $21$ by $3$ .

$7 x < 63$

Divide each term in $7 x < 63$ by $7$ and simplify.

Divide each term in $7 x < 63$ by $7$ .

$\frac{7 x}{7} < \frac{63}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} < \frac{63}{7}$

Divide $x$ by $1$ .

$x < \frac{63}{7}$

Simplify the right side.

Divide $63$ by $7$ .

$x < 9$

The result can be shown in multiple forms.

Inequality Form:

$x < 9$

Interval Notation:

$(- \infty, 9)$

Solve the Inequality for x 2/3x+14-3x>-7

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