Solve for x 5-x/3=(3(x+1))/7

$5 - \frac{x}{3} = \frac{3 (x + 1)}{7}$

Step 1

Multiply both sides by $7$ .

$(5 - \frac{x}{3}) \cdot 7 = \frac{3 (x + 1)}{7} \cdot 7$

Step 2

Simplify.

Simplify the left side.

Simplify $(5 - \frac{x}{3}) \cdot 7$ .

Apply the distributive property.

$5 \cdot 7 - \frac{x}{3} \cdot 7 = \frac{3 (x + 1)}{7} \cdot 7$

Multiply $5$ by $7$ .

$35 - \frac{x}{3} \cdot 7 = \frac{3 (x + 1)}{7} \cdot 7$

Multiply $- \frac{x}{3} \cdot 7$ .

Multiply $7$ by $- 1$ .

$35 - 7 \frac{x}{3} = \frac{3 (x + 1)}{7} \cdot 7$

Combine $- 7$ and $\frac{x}{3}$ .

$35 + \frac{- 7 x}{3} = \frac{3 (x + 1)}{7} \cdot 7$

Move the negative in front of the fraction.

$35 - \frac{7 x}{3} = \frac{3 (x + 1)}{7} \cdot 7$

Reorder $35$ and $- \frac{7 x}{3}$ .

$- \frac{7 x}{3} + 35 = \frac{3 (x + 1)}{7} \cdot 7$

Simplify the right side.

Simplify $\frac{3 (x + 1)}{7} \cdot 7$ .

Cancel the common factor of $7$ .

Cancel the common factor.

$- \frac{7 x}{3} + 35 = \frac{3 (x + 1)}{7} \cdot 7$

Rewrite the expression.

$- \frac{7 x}{3} + 35 = 3 (x + 1)$

Apply the distributive property.

$- \frac{7 x}{3} + 35 = 3 x + 3 \cdot 1$

Multiply $3$ by $1$ .

$- \frac{7 x}{3} + 35 = 3 x + 3$

Step 3

Solve for $x$ .

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

Subtract $3 x$ from both sides of the equation.

$- \frac{7 x}{3} + 35 - 3 x = 3$

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

$- \frac{7 x}{3} - 3 x \cdot \frac{3}{3} + 35 = 3$

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

$- \frac{7 x}{3} + \frac{- 3 x \cdot 3}{3} + 35 = 3$

Combine the numerators over the common denominator.

$\frac{- 7 x - 3 x \cdot 3}{3} + 35 = 3$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- 7 x - 3 x \cdot 3$ .

Factor $x$ out of $- 7 x$ .

$\frac{x \cdot - 7 - 3 x \cdot 3}{3} + 35 = 3$

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

$\frac{x \cdot - 7 + x (- 3 \cdot 3)}{3} + 35 = 3$

Factor $x$ out of $x \cdot - 7 + x (- 3 \cdot 3)$ .

$\frac{x (- 7 - 3 \cdot 3)}{3} + 35 = 3$

Multiply $- 3$ by $3$ .

$\frac{x (- 7 - 9)}{3} + 35 = 3$

Subtract $9$ from $- 7$ .

$\frac{x \cdot - 16}{3} + 35 = 3$

Move $- 16$ to the left of $x$ .

$\frac{- 16 \cdot x}{3} + 35 = 3$

Move the negative in front of the fraction.

$- \frac{16 x}{3} + 35 = 3$

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

Subtract $35$ from both sides of the equation.

$- \frac{16 x}{3} = 3 - 35$

Subtract $35$ from $3$ .

$- \frac{16 x}{3} = - 32$

Multiply both sides of the equation by $- \frac{3}{16}$ .

$- \frac{3}{16} (- \frac{16 x}{3}) = - \frac{3}{16} \cdot - 32$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{3}{16} (- \frac{16 x}{3})$ .

Cancel the common factor of $3$ .

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

$\frac{- 3}{16} (- \frac{16 x}{3}) = - \frac{3}{16} \cdot - 32$

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

$\frac{- 3}{16} \cdot \frac{- 16 x}{3} = - \frac{3}{16} \cdot - 32$

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{16} \cdot \frac{- 16 x}{3} = - \frac{3}{16} \cdot - 32$

Cancel the common factor.

$\frac{3 \cdot - 1}{16} \cdot \frac{- 16 x}{3} = - \frac{3}{16} \cdot - 32$

Rewrite the expression.

$\frac{- 1}{16} (- 16 x) = - \frac{3}{16} \cdot - 32$

Cancel the common factor of $16$ .

Factor $16$ out of $- 16 x$ .

$\frac{- 1}{16} (16 (- x)) = - \frac{3}{16} \cdot - 32$

Cancel the common factor.

$\frac{- 1}{16} (16 (- x)) = - \frac{3}{16} \cdot - 32$

Rewrite the expression.

$- - x = - \frac{3}{16} \cdot - 32$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{3}{16} \cdot - 32$

Multiply $x$ by $1$ .

$x = - \frac{3}{16} \cdot - 32$

Simplify the right side.

Simplify $- \frac{3}{16} \cdot - 32$ .

Cancel the common factor of $16$ .

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

$x = \frac{- 3}{16} \cdot - 32$

Factor $16$ out of $- 32$ .

$x = \frac{- 3}{16} \cdot (16 (- 2))$

Cancel the common factor.

$x = \frac{- 3}{16} \cdot (16 \cdot - 2)$

Rewrite the expression.

$x = - 3 \cdot - 2$

Multiply $- 3$ by $- 2$ .

$x = 6$

Solve for x 5-x/3=(3(x+1))/7

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