Solve for x 32/60=(2x+6)/52.5

$\frac{32}{60} = \frac{2 x + 6}{52.5}$

Step 1

Rewrite the equation as $\frac{2 x + 6}{52.5} = \frac{32}{60}$ .

$\frac{2 x + 6}{52.5} = \frac{32}{60}$

Step 2

Multiply both sides by $52.5$ .

$\frac{2 x + 6}{52.5} \cdot 52.5 = \frac{32}{60} \cdot 52.5$

Step 3

Simplify.

Simplify the left side.

Simplify $\frac{2 x + 6}{52.5} \cdot 52.5$ .

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

Factor $2$ out of $2 x$ .

$\frac{2 (x) + 6}{52.5} \cdot 52.5 = \frac{32}{60} \cdot 52.5$

Factor $2$ out of $6$ .

$\frac{2 x + 2 \cdot 3}{52.5} \cdot 52.5 = \frac{32}{60} \cdot 52.5$

Factor $2$ out of $2 x + 2 \cdot 3$ .

$\frac{2 (x + 3)}{52.5} \cdot 52.5 = \frac{32}{60} \cdot 52.5$

Cancel the common factor of $52.5$ .

Cancel the common factor.

$\frac{2 (x + 3)}{52.5} \cdot 52.5 = \frac{32}{60} \cdot 52.5$

Rewrite the expression.

$2 (x + 3) = \frac{32}{60} \cdot 52.5$

Apply the distributive property.

$2 x + 2 \cdot 3 = \frac{32}{60} \cdot 52.5$

Multiply $2$ by $3$ .

$2 x + 6 = \frac{32}{60} \cdot 52.5$

Simplify the right side.

Simplify $\frac{32}{60} \cdot 52.5$ .

Cancel the common factor of $32$ and $60$ .

Factor $4$ out of $32$ .

$2 x + 6 = \frac{4 (8)}{60} \cdot 52.5$

Cancel the common factors.

Factor $4$ out of $60$ .

$2 x + 6 = \frac{4 \cdot 8}{4 \cdot 15} \cdot 52.5$

Cancel the common factor.

$2 x + 6 = \frac{4 \cdot 8}{4 \cdot 15} \cdot 52.5$

Rewrite the expression.

$2 x + 6 = \frac{8}{15} \cdot 52.5$

Multiply $\frac{8}{15} \cdot 52.5$ .

Combine $\frac{8}{15}$ and $52.5$ .

$2 x + 6 = \frac{8 \cdot 52.5}{15}$

Multiply $8$ by $52.5$ .

$2 x + 6 = \frac{420}{15}$

Divide $420$ by $15$ .

$2 x + 6 = 28$

Step 4

Solve for $x$ .

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

Subtract $6$ from both sides of the equation.

$2 x = 28 - 6$

Subtract $6$ from $28$ .

$2 x = 22$

Divide each term in $2 x = 22$ by $2$ and simplify.

Divide each term in $2 x = 22$ by $2$ .

$\frac{2 x}{2} = \frac{22}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{22}{2}$

Divide $x$ by $1$ .

$x = \frac{22}{2}$

Simplify the right side.

Divide $22$ by $2$ .

$x = 11$

Solve for x 32/60=(2x+6)/52.5

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