Solve for x 2/3x+5=-3x-3

$\frac{2}{3} x + 5 = - 3 x - 3$

Step 1

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

$\frac{2 x}{3} + 5 = - 3 x - 3$

Step 2

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

Add $3 x$ to both sides of the equation.

$\frac{2 x}{3} + 5 + 3 x = - 3$

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

$\frac{2 x}{3} + 3 x \cdot \frac{3}{3} + 5 = - 3$

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

$\frac{2 x}{3} + \frac{3 x \cdot 3}{3} + 5 = - 3$

Combine the numerators over the common denominator.

$\frac{2 x + 3 x \cdot 3}{3} + 5 = - 3$

Simplify each term.

Simplify the numerator.

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

Factor $x$ out of $2 x$ .

$\frac{x \cdot 2 + 3 x \cdot 3}{3} + 5 = - 3$

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

$\frac{x \cdot 2 + x (3 \cdot 3)}{3} + 5 = - 3$

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

$\frac{x (2 + 3 \cdot 3)}{3} + 5 = - 3$

Multiply $3$ by $3$ .

$\frac{x (2 + 9)}{3} + 5 = - 3$

Add $2$ and $9$ .

$\frac{x \cdot 11}{3} + 5 = - 3$

Move $11$ to the left of $x$ .

$\frac{11 x}{3} + 5 = - 3$

Step 3

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

Subtract $5$ from both sides of the equation.

$\frac{11 x}{3} = - 3 - 5$

Subtract $5$ from $- 3$ .

$\frac{11 x}{3} = - 8$

Step 4

Multiply both sides of the equation by $\frac{3}{11}$ .

$\frac{3}{11} \cdot \frac{11 x}{3} = \frac{3}{11} \cdot - 8$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{11} \cdot \frac{11 x}{3}$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{11} \cdot \frac{11 x}{3} = \frac{3}{11} \cdot - 8$

Rewrite the expression.

$\frac{1}{11} (11 x) = \frac{3}{11} \cdot - 8$

Cancel the common factor of $11$ .

Factor $11$ out of $11 x$ .

$\frac{1}{11} (11 (x)) = \frac{3}{11} \cdot - 8$

Cancel the common factor.

$\frac{1}{11} (11 x) = \frac{3}{11} \cdot - 8$

Rewrite the expression.

$x = \frac{3}{11} \cdot - 8$

Simplify the right side.

Simplify $\frac{3}{11} \cdot - 8$ .

Multiply $\frac{3}{11} \cdot - 8$ .

Combine $\frac{3}{11}$ and $- 8$ .

$x = \frac{3 \cdot - 8}{11}$

Multiply $3$ by $- 8$ .

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

Move the negative in front of the fraction.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 2.\overline{18}$

Mixed Number Form:

$x = - 2 \frac{2}{11}$

Solve for x 2/3x+5=-3x-3

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