Solve for a 3/4(2a-6)+1/2=2/5(3a+20)

$\frac{3}{4} (2 a - 6) + \frac{1}{2} = \frac{2}{5} (3 a + 20)$

Simplify $\frac{3}{4} \cdot (2 a - 6) + \frac{1}{2}$ .

Simplify each term.

Apply the distributive property.

$\frac{3}{4} (2 a) + \frac{3}{4} \cdot - 6 + \frac{1}{2} = \frac{2}{5} \cdot (3 a + 20)$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{3}{2 (2)} (2 a) + \frac{3}{4} \cdot - 6 + \frac{1}{2} = \frac{2}{5} \cdot (3 a + 20)$

Factor $2$ out of $2 a$ .

$\frac{3}{2 (2)} (2 (a)) + \frac{3}{4} \cdot - 6 + \frac{1}{2} = \frac{2}{5} \cdot (3 a + 20)$

Cancel the common factor.

$\frac{3}{2 \cdot 2} (2 a) + \frac{3}{4} \cdot - 6 + \frac{1}{2} = \frac{2}{5} \cdot (3 a + 20)$

Rewrite the expression.

$\frac{3}{2} a + \frac{3}{4} \cdot - 6 + \frac{1}{2} = \frac{2}{5} \cdot (3 a + 20)$

Combine $\frac{3}{2}$ and $a$ .

$\frac{3 a}{2} + \frac{3}{4} \cdot - 6 + \frac{1}{2} = \frac{2}{5} \cdot (3 a + 20)$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{3 a}{2} + \frac{3}{2 (2)} \cdot - 6 + \frac{1}{2} = \frac{2}{5} \cdot (3 a + 20)$

Factor $2$ out of $- 6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Combine $\frac{3}{2}$ and $- 3$ .

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

Multiply $3$ by $- 3$ .

$\frac{3 a}{2} + \frac{- 9}{2} + \frac{1}{2} = \frac{2}{5} \cdot (3 a + 20)$

Move the negative in front of the fraction.

$\frac{3 a}{2} - \frac{9}{2} + \frac{1}{2} = \frac{2}{5} \cdot (3 a + 20)$

Combine fractions.

Combine the numerators over the common denominator.

$\frac{3 a - 9 + 1}{2} = \frac{2}{5} \cdot (3 a + 20)$

Add $- 9$ and $1$ .

$\frac{3 a - 8}{2} = \frac{2}{5} \cdot (3 a + 20)$

Simplify $\frac{2}{5} \cdot (3 a + 20)$ .

Apply the distributive property.

$\frac{3 a - 8}{2} = \frac{2}{5} (3 a) + \frac{2}{5} \cdot 20$

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

Combine $3$ and $\frac{2}{5}$ .

$\frac{3 a - 8}{2} = \frac{3 \cdot 2}{5} a + \frac{2}{5} \cdot 20$

Multiply $3$ by $2$ .

$\frac{3 a - 8}{2} = \frac{6}{5} a + \frac{2}{5} \cdot 20$

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

$\frac{3 a - 8}{2} = \frac{6 a}{5} + \frac{2}{5} \cdot 20$

Cancel the common factor of $5$ .

Factor $5$ out of $20$ .

$\frac{3 a - 8}{2} = \frac{6 a}{5} + \frac{2}{5} \cdot (5 (4))$

Cancel the common factor.

$\frac{3 a - 8}{2} = \frac{6 a}{5} + \frac{2}{5} \cdot (5 \cdot 4)$

Rewrite the expression.

$\frac{3 a - 8}{2} = \frac{6 a}{5} + 2 \cdot 4$

Multiply $2$ by $4$ .

$\frac{3 a - 8}{2} = \frac{6 a}{5} + 8$

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

Subtract $\frac{6 a}{5}$ from both sides of the equation.

$\frac{3 a - 8}{2} - \frac{6 a}{5} = 8$

To write $\frac{3 a - 8}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3 a - 8}{2} \cdot \frac{5}{5} - \frac{6 a}{5} = 8$

To write $- \frac{6 a}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 a - 8}{2} \cdot \frac{5}{5} - \frac{6 a}{5} \cdot \frac{2}{2} = 8$

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3 a - 8}{2}$ by $\frac{5}{5}$ .

$\frac{(3 a - 8) \cdot 5}{2 \cdot 5} - \frac{6 a}{5} \cdot \frac{2}{2} = 8$

Multiply $2$ by $5$ .

$\frac{(3 a - 8) \cdot 5}{10} - \frac{6 a}{5} \cdot \frac{2}{2} = 8$

Multiply $\frac{6 a}{5}$ by $\frac{2}{2}$ .

$\frac{(3 a - 8) \cdot 5}{10} - \frac{6 a \cdot 2}{5 \cdot 2} = 8$

Multiply $5$ by $2$ .

$\frac{(3 a - 8) \cdot 5}{10} - \frac{6 a \cdot 2}{10} = 8$

Combine the numerators over the common denominator.

$\frac{(3 a - 8) \cdot 5 - 6 a \cdot 2}{10} = 8$

Simplify the numerator.

Apply the distributive property.

$\frac{3 a \cdot 5 - 8 \cdot 5 - 6 a \cdot 2}{10} = 8$

Multiply $5$ by $3$ .

$\frac{15 a - 8 \cdot 5 - 6 a \cdot 2}{10} = 8$

Multiply $- 8$ by $5$ .

$\frac{15 a - 40 - 6 a \cdot 2}{10} = 8$

Multiply $2$ by $- 6$ .

$\frac{15 a - 40 - 12 a}{10} = 8$

Subtract $12 a$ from $15 a$ .

$\frac{3 a - 40}{10} = 8$

Multiply both sides by $10$ .

$\frac{3 a - 40}{10} \cdot 10 = 8 \cdot 10$

Simplify.

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{3 a - 40}{10} \cdot 10 = 8 \cdot 10$

Rewrite the expression.

$3 a - 40 = 8 \cdot 10$

Simplify the right side.

Multiply $8$ by $10$ .

$3 a - 40 = 80$

Solve for $a$ .

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

Add $40$ to both sides of the equation.

$3 a = 80 + 40$

Add $80$ and $40$ .

$3 a = 120$

Divide each term in $3 a = 120$ by $3$ and simplify.

Divide each term in $3 a = 120$ by $3$ .

$\frac{3 a}{3} = \frac{120}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 a}{3} = \frac{120}{3}$

Divide $a$ by $1$ .

$a = \frac{120}{3}$

Simplify the right side.

Divide $120$ by $3$ .

$a = 40$

Solve for a 3/4(2a-6)+1/2=2/5(3a+20)

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