Solve the Inequality for x -3(2x+2)<10

$- 3 (2 x + 2) < 10$

Divide each term in $- 3 (2 x + 2) < 10$ by $- 3$ and simplify.

Divide each term in $- 3 (2 x + 2) < 10$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 (2 x + 2)}{- 3} > \frac{10}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 (2 x + 2)}{- 3} > \frac{10}{- 3}$

Divide $2 x + 2$ by $1$ .

$2 x + 2 > \frac{10}{- 3}$

Simplify the right side.

Move the negative in front of the fraction.

$2 x + 2 > - \frac{10}{3}$

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

Subtract $2$ from both sides of the inequality.

$2 x > - \frac{10}{3} - 2$

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$2 x > - \frac{10}{3} - 2 \cdot \frac{3}{3}$

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

$2 x > - \frac{10}{3} + \frac{- 2 \cdot 3}{3}$

Combine the numerators over the common denominator.

$2 x > \frac{- 10 - 2 \cdot 3}{3}$

Simplify the numerator.

Multiply $- 2$ by $3$ .

$2 x > \frac{- 10 - 6}{3}$

Subtract $6$ from $- 10$ .

$2 x > \frac{- 16}{3}$

Move the negative in front of the fraction.

$2 x > - \frac{16}{3}$

Divide each term in $2 x > - \frac{16}{3}$ by $2$ and simplify.

Divide each term in $2 x > - \frac{16}{3}$ by $2$ .

$\frac{2 x}{2} > \frac{- \frac{16}{3}}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} > \frac{- \frac{16}{3}}{2}$

Divide $x$ by $1$ .

$x > \frac{- \frac{16}{3}}{2}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x > - \frac{16}{3} \cdot \frac{1}{2}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{16}{3}$ into the numerator.

$x > \frac{- 16}{3} \cdot \frac{1}{2}$

Factor $2$ out of $- 16$ .

$x > \frac{2 (- 8)}{3} \cdot \frac{1}{2}$

Cancel the common factor.

$x > \frac{2 \cdot - 8}{3} \cdot \frac{1}{2}$

Rewrite the expression.

$x > \frac{- 8}{3}$

Move the negative in front of the fraction.

$x > - \frac{8}{3}$

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{8}{3}$

Interval Notation:

$(- \frac{8}{3}, \infty)$

Solve the Inequality for x -3(2x+2)<10

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