Solve for x 3(2x-5)=3/5(6x-1)

$3 (2 x - 5) = \frac{3}{5} (6 x - 1)$

Step 1

Simplify $3 (2 x - 5)$ .

Start simplifying.

$0 + 0 + 3 (2 x - 5) = \frac{3}{5} \cdot (6 x - 1)$

Simplify by adding zeros.

$3 (2 x - 5) = \frac{3}{5} \cdot (6 x - 1)$

Apply the distributive property.

$3 (2 x) + 3 \cdot - 5 = \frac{3}{5} \cdot (6 x - 1)$

Multiply.

Multiply $2$ by $3$ .

$6 x + 3 \cdot - 5 = \frac{3}{5} \cdot (6 x - 1)$

Multiply $3$ by $- 5$ .

$6 x - 15 = \frac{3}{5} \cdot (6 x - 1)$

Step 2

Simplify $\frac{3}{5} \cdot (6 x - 1)$ .

Apply the distributive property.

$6 x - 15 = \frac{3}{5} (6 x) + \frac{3}{5} \cdot - 1$

Multiply $\frac{3}{5} (6 x)$ .

Combine $6$ and $\frac{3}{5}$ .

$6 x - 15 = \frac{6 \cdot 3}{5} x + \frac{3}{5} \cdot - 1$

Multiply $6$ by $3$ .

$6 x - 15 = \frac{18}{5} x + \frac{3}{5} \cdot - 1$

Combine $\frac{18}{5}$ and $x$ .

$6 x - 15 = \frac{18 x}{5} + \frac{3}{5} \cdot - 1$

Multiply $\frac{3}{5} \cdot - 1$ .

Combine $\frac{3}{5}$ and $- 1$ .

$6 x - 15 = \frac{18 x}{5} + \frac{3 \cdot - 1}{5}$

Multiply $3$ by $- 1$ .

$6 x - 15 = \frac{18 x}{5} + \frac{- 3}{5}$

Move the negative in front of the fraction.

$6 x - 15 = \frac{18 x}{5} - \frac{3}{5}$

Step 3

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

Subtract $\frac{18 x}{5}$ from both sides of the equation.

$6 x - 15 - \frac{18 x}{5} = - \frac{3}{5}$

To write $6 x$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$6 x \cdot \frac{5}{5} - \frac{18 x}{5} - 15 = - \frac{3}{5}$

Combine $6 x$ and $\frac{5}{5}$ .

$\frac{6 x \cdot 5}{5} - \frac{18 x}{5} - 15 = - \frac{3}{5}$

Combine the numerators over the common denominator.

$\frac{6 x \cdot 5 - 18 x}{5} - 15 = - \frac{3}{5}$

Simplify the numerator.

Factor $6 x$ out of $6 x \cdot 5 - 18 x$ .

Factor $6 x$ out of $6 x \cdot 5$ .

$\frac{6 x (5) - 18 x}{5} - 15 = - \frac{3}{5}$

Factor $6 x$ out of $- 18 x$ .

$\frac{6 x (5) + 6 x (- 3)}{5} - 15 = - \frac{3}{5}$

Factor $6 x$ out of $6 x (5) + 6 x (- 3)$ .

$\frac{6 x (5 - 3)}{5} - 15 = - \frac{3}{5}$

Subtract $3$ from $5$ .

$\frac{6 x \cdot 2}{5} - 15 = - \frac{3}{5}$

Multiply $2$ by $6$ .

$\frac{12 x}{5} - 15 = - \frac{3}{5}$

Step 4

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

Add $15$ to both sides of the equation.

$\frac{12 x}{5} = - \frac{3}{5} + 15$

To write $15$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{12 x}{5} = - \frac{3}{5} + 15 \cdot \frac{5}{5}$

Combine $15$ and $\frac{5}{5}$ .

$\frac{12 x}{5} = - \frac{3}{5} + \frac{15 \cdot 5}{5}$

Combine the numerators over the common denominator.

$\frac{12 x}{5} = \frac{- 3 + 15 \cdot 5}{5}$

Simplify the numerator.

Multiply $15$ by $5$ .

$\frac{12 x}{5} = \frac{- 3 + 75}{5}$

Add $- 3$ and $75$ .

$\frac{12 x}{5} = \frac{72}{5}$

Step 5

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$12 x = 72$

Step 6

Divide each term in $12 x = 72$ by $12$ and simplify.

Divide each term in $12 x = 72$ by $12$ .

$\frac{12 x}{12} = \frac{72}{12}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 x}{12} = \frac{72}{12}$

Divide $x$ by $1$ .

$x = \frac{72}{12}$

Simplify the right side.

Divide $72$ by $12$ .

$x = 6$

Solve for x 3(2x-5)=3/5(6x-1)

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