Solve for x (4x+4)/48=(7x-9)/60

$\frac{4 x + 4}{48} = \frac{7 x - 9}{60}$

Step 1

Cancel the common factor of $4 x + 4$ and $48$ .

Factor $4$ out of $4 x$ .

$\frac{4 (x) + 4}{48} = \frac{7 x - 9}{60}$

Factor $4$ out of $4$ .

$\frac{4 (x) + 4 (1)}{48} = \frac{7 x - 9}{60}$

Factor $4$ out of $4 (x) + 4 (1)$ .

$\frac{4 (x + 1)}{48} = \frac{7 x - 9}{60}$

Cancel the common factors.

Factor $4$ out of $48$ .

$\frac{4 (x + 1)}{4 (12)} = \frac{7 x - 9}{60}$

Cancel the common factor.

$\frac{4 (x + 1)}{4 \cdot 12} = \frac{7 x - 9}{60}$

Rewrite the expression.

$\frac{x + 1}{12} = \frac{7 x - 9}{60}$

Step 2

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$(x + 1) \cdot 60 = 12 (7 x - 9)$

Step 3

Solve the equation for $x$ .

Simplify $(x + 1) \cdot 60$ .

Start simplifying.

$0 + 0 + (x + 1) \cdot 60 = 12 (7 x - 9)$

Simplify by adding zeros.

$(x + 1) \cdot 60 = 12 (7 x - 9)$

Apply the distributive property.

$x \cdot 60 + 1 \cdot 60 = 12 (7 x - 9)$

Simplify the expression.

Move $60$ to the left of $x$ .

$60 \cdot x + 1 \cdot 60 = 12 (7 x - 9)$

Multiply $60$ by $1$ .

$60 x + 60 = 12 (7 x - 9)$

Simplify $12 (7 x - 9)$ .

Apply the distributive property.

$60 x + 60 = 12 (7 x) + 12 \cdot - 9$

Multiply.

Multiply $7$ by $12$ .

$60 x + 60 = 84 x + 12 \cdot - 9$

Multiply $12$ by $- 9$ .

$60 x + 60 = 84 x - 108$

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

Subtract $84 x$ from both sides of the equation.

$60 x + 60 - 84 x = - 108$

Subtract $84 x$ from $60 x$ .

$- 24 x + 60 = - 108$

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

Subtract $60$ from both sides of the equation.

$- 24 x = - 108 - 60$

Subtract $60$ from $- 108$ .

$- 24 x = - 168$

Divide each term in $- 24 x = - 168$ by $- 24$ and simplify.

Divide each term in $- 24 x = - 168$ by $- 24$ .

$\frac{- 24 x}{- 24} = \frac{- 168}{- 24}$

Simplify the left side.

Cancel the common factor of $- 24$ .

Cancel the common factor.

$\frac{- 24 x}{- 24} = \frac{- 168}{- 24}$

Divide $x$ by $1$ .

$x = \frac{- 168}{- 24}$

Simplify the right side.

Divide $- 168$ by $- 24$ .

$x = 7$

Solve for x (4x+4)/48=(7x-9)/60

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