Solve for a (4a-3)/3-(6a-3)/5=2

$\frac{4 a - 3}{3} - \frac{6 a - 3}{5} = 2$

Step 1

Simplify $\frac{4 a - 3}{3} - \frac{6 a - 3}{5}$ .

Factor $3$ out of $6 a - 3$ .

Factor $3$ out of $6 a$ .

$\frac{4 a - 3}{3} - \frac{3 (2 a) - 3}{5} = 2$

Factor $3$ out of $- 3$ .

$\frac{4 a - 3}{3} - \frac{3 (2 a) + 3 (- 1)}{5} = 2$

Factor $3$ out of $3 (2 a) + 3 (- 1)$ .

$\frac{4 a - 3}{3} - \frac{3 (2 a - 1)}{5} = 2$

To write $\frac{4 a - 3}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{4 a - 3}{3} \cdot \frac{5}{5} - \frac{3 (2 a - 1)}{5} = 2$

To write $- \frac{3 (2 a - 1)}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{4 a - 3}{3} \cdot \frac{5}{5} - \frac{3 (2 a - 1)}{5} \cdot \frac{3}{3} = 2$

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4 a - 3}{3}$ by $\frac{5}{5}$ .

$\frac{(4 a - 3) \cdot 5}{3 \cdot 5} - \frac{3 (2 a - 1)}{5} \cdot \frac{3}{3} = 2$

Multiply $3$ by $5$ .

$\frac{(4 a - 3) \cdot 5}{15} - \frac{3 (2 a - 1)}{5} \cdot \frac{3}{3} = 2$

Multiply $\frac{3 (2 a - 1)}{5}$ by $\frac{3}{3}$ .

$\frac{(4 a - 3) \cdot 5}{15} - \frac{3 (2 a - 1) \cdot 3}{5 \cdot 3} = 2$

Multiply $5$ by $3$ .

$\frac{(4 a - 3) \cdot 5}{15} - \frac{3 (2 a - 1) \cdot 3}{15} = 2$

Combine the numerators over the common denominator.

$\frac{(4 a - 3) \cdot 5 - 3 (2 a - 1) \cdot 3}{15} = 2$

Simplify the numerator.

Apply the distributive property.

$\frac{4 a \cdot 5 - 3 \cdot 5 - 3 (2 a - 1) \cdot 3}{15} = 2$

Multiply $5$ by $4$ .

$\frac{20 a - 3 \cdot 5 - 3 (2 a - 1) \cdot 3}{15} = 2$

Multiply $- 3$ by $5$ .

$\frac{20 a - 15 - 3 (2 a - 1) \cdot 3}{15} = 2$

Apply the distributive property.

$\frac{20 a - 15 + (- 3 (2 a) - 3 \cdot - 1) \cdot 3}{15} = 2$

Multiply $2$ by $- 3$ .

$\frac{20 a - 15 + (- 6 a - 3 \cdot - 1) \cdot 3}{15} = 2$

Multiply $- 3$ by $- 1$ .

$\frac{20 a - 15 + (- 6 a + 3) \cdot 3}{15} = 2$

Apply the distributive property.

$\frac{20 a - 15 - 6 a \cdot 3 + 3 \cdot 3}{15} = 2$

Multiply $3$ by $- 6$ .

$\frac{20 a - 15 - 18 a + 3 \cdot 3}{15} = 2$

Multiply $3$ by $3$ .

$\frac{20 a - 15 - 18 a + 9}{15} = 2$

Subtract $18 a$ from $20 a$ .

$\frac{2 a - 15 + 9}{15} = 2$

Add $- 15$ and $9$ .

$\frac{2 a - 6}{15} = 2$

Factor $2$ out of $2 a - 6$ .

Factor $2$ out of $2 a$ .

$\frac{2 (a) - 6}{15} = 2$

Factor $2$ out of $- 6$ .

$\frac{2 a + 2 \cdot - 3}{15} = 2$

Factor $2$ out of $2 a + 2 \cdot - 3$ .

$\frac{2 (a - 3)}{15} = 2$

Step 2

Multiply both sides of the equation by $\frac{15}{2}$ .

$\frac{15}{2} \cdot \frac{2 (a - 3)}{15} = \frac{15}{2} \cdot 2$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{15}{2} \cdot \frac{2 (a - 3)}{15}$ .

Cancel the common factor of $15$ .

Cancel the common factor.

$\frac{15}{2} \cdot \frac{2 (a - 3)}{15} = \frac{15}{2} \cdot 2$

Rewrite the expression.

$\frac{1}{2} (2 (a - 3)) = \frac{15}{2} \cdot 2$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{1}{2} (2 (a - 3)) = \frac{15}{2} \cdot 2$

Rewrite the expression.

$a - 3 = \frac{15}{2} \cdot 2$

Simplify the right side.

Cancel the common factor of $2$ .

Cancel the common factor.

$a - 3 = \frac{15}{2} \cdot 2$

Rewrite the expression.

$a - 3 = 15$

Step 4

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

Add $3$ to both sides of the equation.

$a = 15 + 3$

Add $15$ and $3$ .

$a = 18$

Solve for a (4a-3)/3-(6a-3)/5=2

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