Solve for x 3/5(x+2)=x-4

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

Step 1

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

Rewrite.

$0 + 0 + \frac{3}{5} \cdot (x + 2) = x - 4$

Simplify by adding zeros.

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

Apply the distributive property.

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

Combine $\frac{3}{5}$ and $x$ .

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

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

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

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

Multiply $3$ by $2$ .

$\frac{3 x}{5} + \frac{6}{5} = x - 4$

Step 2

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

Subtract $x$ from both sides of the equation.

$\frac{3 x}{5} + \frac{6}{5} - x = - 4$

To write $- x$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3 x}{5} - x \cdot \frac{5}{5} + \frac{6}{5} = - 4$

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

$\frac{3 x}{5} + \frac{- x \cdot 5}{5} + \frac{6}{5} = - 4$

Combine the numerators over the common denominator.

$\frac{3 x - x \cdot 5}{5} + \frac{6}{5} = - 4$

Combine the numerators over the common denominator.

$\frac{3 x - x \cdot 5 + 6}{5} = - 4$

Multiply $5$ by $- 1$ .

$\frac{3 x - 5 x + 6}{5} = - 4$

Subtract $5 x$ from $3 x$ .

$\frac{- 2 x + 6}{5} = - 4$

Factor $2$ out of $- 2 x + 6$ .

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

$\frac{2 (- x) + 6}{5} = - 4$

Factor $2$ out of $6$ .

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

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

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

Factor $- 1$ out of $- x$ .

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

Rewrite $3$ as $- 1 (- 3)$ .

$\frac{2 (- (x) - 1 (- 3))}{5} = - 4$

Factor $- 1$ out of $- (x) - 1 (- 3)$ .

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

Rewrite $- (x - 3)$ as $- 1 (x - 3)$ .

$\frac{2 (- 1 (x - 3))}{5} = - 4$

Move the negative in front of the fraction.

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

Step 3

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

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

Step 4

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $5$ .

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

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

Move the leading negative in $- \frac{2 (x - 3)}{5}$ into the numerator.

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

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{2} \cdot \frac{- 2 (x - 3)}{5} = - \frac{5}{2} \cdot - 4$

Cancel the common factor.

$\frac{5 \cdot - 1}{2} \cdot \frac{- 2 (x - 3)}{5} = - \frac{5}{2} \cdot - 4$

Rewrite the expression.

$\frac{- 1}{2} (- 2 (x - 3)) = - \frac{5}{2} \cdot - 4$

Cancel the common factor of $2$ .

Factor $2$ out of $- 2 (x - 3)$ .

$\frac{- 1}{2} (2 (- (x - 3))) = - \frac{5}{2} \cdot - 4$

Cancel the common factor.

$\frac{- 1}{2} (2 (- (x - 3))) = - \frac{5}{2} \cdot - 4$

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (x - 3) = - \frac{5}{2} \cdot - 4$

Multiply $x - 3$ by $1$ .

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

Simplify the right side.

Simplify $- \frac{5}{2} \cdot - 4$ .

Cancel the common factor of $2$ .

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

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

Factor $2$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x - 3 = - 5 \cdot - 2$

Multiply $- 5$ by $- 2$ .

$x - 3 = 10$

Step 5

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

Add $3$ to both sides of the equation.

$x = 10 + 3$

Add $10$ and $3$ .

$x = 13$

Solve for x 3/5(x+2)=x-4

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