Solve for x 1/5(5x-5)+3x=-9(1/3x+4)

$\frac{1}{5} (5 x - 5) + 3 x = - 9 (\frac{1}{3} x + 4)$

Step 1

Simplify $\frac{1}{5} \cdot (5 x - 5) + 3 x$ .

Simplify each term.

Apply the distributive property.

$\frac{1}{5} (5 x) + \frac{1}{5} \cdot - 5 + 3 x = - 9 (\frac{1}{3} x + 4)$

Cancel the common factor of $5$ .

Factor $5$ out of $5 x$ .

$\frac{1}{5} (5 (x)) + \frac{1}{5} \cdot - 5 + 3 x = - 9 (\frac{1}{3} x + 4)$

Cancel the common factor.

$\frac{1}{5} (5 x) + \frac{1}{5} \cdot - 5 + 3 x = - 9 (\frac{1}{3} x + 4)$

Rewrite the expression.

$x + \frac{1}{5} \cdot - 5 + 3 x = - 9 (\frac{1}{3} x + 4)$

Cancel the common factor of $5$ .

Factor $5$ out of $- 5$ .

$x + \frac{1}{5} \cdot (5 (- 1)) + 3 x = - 9 (\frac{1}{3} x + 4)$

Cancel the common factor.

$x + \frac{1}{5} \cdot (5 \cdot - 1) + 3 x = - 9 (\frac{1}{3} x + 4)$

Rewrite the expression.

$x - 1 + 3 x = - 9 (\frac{1}{3} x + 4)$

Add $x$ and $3 x$ .

$4 x - 1 = - 9 (\frac{1}{3} x + 4)$

Step 2

Simplify $- 9 (\frac{1}{3} x + 4)$ .

Combine $\frac{1}{3}$ and $x$ .

$4 x - 1 = - 9 (\frac{x}{3} + 4)$

Apply the distributive property.

$4 x - 1 = - 9 \frac{x}{3} - 9 \cdot 4$

Cancel the common factor of $3$ .

Factor $3$ out of $- 9$ .

$4 x - 1 = 3 (- 3) \frac{x}{3} - 9 \cdot 4$

Cancel the common factor.

$4 x - 1 = 3 \cdot - 3 \frac{x}{3} - 9 \cdot 4$

Rewrite the expression.

$4 x - 1 = - 3 x - 9 \cdot 4$

Multiply $- 9$ by $4$ .

$4 x - 1 = - 3 x - 36$

Step 3

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

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

$4 x - 1 + 3 x = - 36$

Add $4 x$ and $3 x$ .

$7 x - 1 = - 36$

Step 4

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

Add $1$ to both sides of the equation.

$7 x = - 36 + 1$

Add $- 36$ and $1$ .

$7 x = - 35$

Step 5

Divide each term in $7 x = - 35$ by $7$ and simplify.

Divide each term in $7 x = - 35$ by $7$ .

$\frac{7 x}{7} = \frac{- 35}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 35}{7}$

Divide $x$ by $1$ .

$x = \frac{- 35}{7}$

Simplify the right side.

Divide $- 35$ by $7$ .

$x = - 5$

Solve for x 1/5(5x-5)+3x=-9(1/3x+4)

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