Solve for x -2/5(x+3)=8

$- \frac{2}{5} (x + 3) = 8$

Step 1

Multiply both sides of the equation by $- \frac{5}{2}$ .

$- \frac{5}{2} (- \frac{2}{5} \cdot (x + 3)) = - \frac{5}{2} \cdot 8$

Step 2

Simplify both sides of the equation.

Simplify the left side.

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

Apply the distributive property.

$- \frac{5}{2} (- \frac{2}{5} x - \frac{2}{5} \cdot 3) = - \frac{5}{2} \cdot 8$

Combine $x$ and $\frac{2}{5}$ .

$- \frac{5}{2} (- \frac{x \cdot 2}{5} - \frac{2}{5} \cdot 3) = - \frac{5}{2} \cdot 8$

Multiply $- \frac{2}{5} \cdot 3$ .

Multiply $3$ by $- 1$ .

$- \frac{5}{2} (- \frac{x \cdot 2}{5} - 3 (\frac{2}{5})) = - \frac{5}{2} \cdot 8$

Combine $- 3$ and $\frac{2}{5}$ .

$- \frac{5}{2} (- \frac{x \cdot 2}{5} + \frac{- 3 \cdot 2}{5}) = - \frac{5}{2} \cdot 8$

Multiply $- 3$ by $2$ .

$- \frac{5}{2} (- \frac{x \cdot 2}{5} + \frac{- 6}{5}) = - \frac{5}{2} \cdot 8$

Simplify each term.

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

$- \frac{5}{2} (- \frac{2 \cdot x}{5} + \frac{- 6}{5}) = - \frac{5}{2} \cdot 8$

Move the negative in front of the fraction.

$- \frac{5}{2} (- \frac{2 x}{5} - \frac{6}{5}) = - \frac{5}{2} \cdot 8$

Simplify terms.

Apply the distributive property.

$- \frac{5}{2} (- \frac{2 x}{5}) - \frac{5}{2} (- \frac{6}{5}) = - \frac{5}{2} \cdot 8$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$\frac{- 5}{2} (- \frac{2 x}{5}) - \frac{5}{2} (- \frac{6}{5}) = - \frac{5}{2} \cdot 8$

Move the leading negative in $- \frac{2 x}{5}$ into the numerator.

$\frac{- 5}{2} \cdot \frac{- 2 x}{5} - \frac{5}{2} (- \frac{6}{5}) = - \frac{5}{2} \cdot 8$

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{2} \cdot \frac{- 2 x}{5} - \frac{5}{2} (- \frac{6}{5}) = - \frac{5}{2} \cdot 8$

Cancel the common factor.

$\frac{5 \cdot - 1}{2} \cdot \frac{- 2 x}{5} - \frac{5}{2} (- \frac{6}{5}) = - \frac{5}{2} \cdot 8$

Rewrite the expression.

$\frac{- 1}{2} (- 2 x) - \frac{5}{2} (- \frac{6}{5}) = - \frac{5}{2} \cdot 8$

Cancel the common factor of $2$ .

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

$\frac{- 1}{2} (2 (- x)) - \frac{5}{2} (- \frac{6}{5}) = - \frac{5}{2} \cdot 8$

Cancel the common factor.

$\frac{- 1}{2} (2 (- x)) - \frac{5}{2} (- \frac{6}{5}) = - \frac{5}{2} \cdot 8$

Rewrite the expression.

$- - x - \frac{5}{2} (- \frac{6}{5}) = - \frac{5}{2} \cdot 8$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x - \frac{5}{2} (- \frac{6}{5}) = - \frac{5}{2} \cdot 8$

Multiply $x$ by $1$ .

$x - \frac{5}{2} (- \frac{6}{5}) = - \frac{5}{2} \cdot 8$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$x + \frac{- 5}{2} (- \frac{6}{5}) = - \frac{5}{2} \cdot 8$

Move the leading negative in $- \frac{6}{5}$ into the numerator.

$x + \frac{- 5}{2} \cdot \frac{- 6}{5} = - \frac{5}{2} \cdot 8$

Factor $5$ out of $- 5$ .

$x + \frac{5 (- 1)}{2} \cdot \frac{- 6}{5} = - \frac{5}{2} \cdot 8$

Cancel the common factor.

$x + \frac{5 \cdot - 1}{2} \cdot \frac{- 6}{5} = - \frac{5}{2} \cdot 8$

Rewrite the expression.

$x + \frac{- 1}{2} \cdot - 6 = - \frac{5}{2} \cdot 8$

Cancel the common factor of $2$ .

Factor $2$ out of $- 6$ .

$x + \frac{- 1}{2} \cdot (2 (- 3)) = - \frac{5}{2} \cdot 8$

Cancel the common factor.

$x + \frac{- 1}{2} \cdot (2 \cdot - 3) = - \frac{5}{2} \cdot 8$

Rewrite the expression.

$x - - 3 = - \frac{5}{2} \cdot 8$

Multiply $- 1$ by $- 3$ .

$x + 3 = - \frac{5}{2} \cdot 8$

Simplify the right side.

Simplify $- \frac{5}{2} \cdot 8$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$x + 3 = \frac{- 5}{2} \cdot 8$

Factor $2$ out of $8$ .

$x + 3 = \frac{- 5}{2} \cdot (2 (4))$

Cancel the common factor.

$x + 3 = \frac{- 5}{2} \cdot (2 \cdot 4)$

Rewrite the expression.

$x + 3 = - 5 \cdot 4$

Multiply $- 5$ by $4$ .

$x + 3 = - 20$

Step 3

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

Subtract $3$ from both sides of the equation.

$x = - 20 - 3$

Subtract $3$ from $- 20$ .

$x = - 23$

Solve for x -2/5(x+3)=8

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