Evaluate (4a)/5+3/2-a/4=(7a)/10

$\frac{4 a}{5} + \frac{3}{2} - \frac{a}{4} = \frac{7 a}{10}$

Step 1

Multiply both sides by $10$ .

$(\frac{4 a}{5} + \frac{3}{2} - \frac{a}{4}) \cdot 10 = \frac{7 a}{10} \cdot 10$

Step 2

Simplify.

Simplify the left side.

Simplify $(\frac{4 a}{5} + \frac{3}{2} - \frac{a}{4}) \cdot 10$ .

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

$(\frac{4 a}{5} \cdot \frac{4}{4} - \frac{a}{4} + \frac{3}{2}) \cdot 10 = \frac{7 a}{10} \cdot 10$

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

$(\frac{4 a}{5} \cdot \frac{4}{4} - \frac{a}{4} \cdot \frac{5}{5} + \frac{3}{2}) \cdot 10 = \frac{7 a}{10} \cdot 10$

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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

$(\frac{4 a \cdot 4}{5 \cdot 4} - \frac{a}{4} \cdot \frac{5}{5} + \frac{3}{2}) \cdot 10 = \frac{7 a}{10} \cdot 10$

Multiply $5$ by $4$ .

$(\frac{4 a \cdot 4}{20} - \frac{a}{4} \cdot \frac{5}{5} + \frac{3}{2}) \cdot 10 = \frac{7 a}{10} \cdot 10$

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

$(\frac{4 a \cdot 4}{20} - \frac{a \cdot 5}{4 \cdot 5} + \frac{3}{2}) \cdot 10 = \frac{7 a}{10} \cdot 10$

Multiply $4$ by $5$ .

$(\frac{4 a \cdot 4}{20} - \frac{a \cdot 5}{20} + \frac{3}{2}) \cdot 10 = \frac{7 a}{10} \cdot 10$

Combine the numerators over the common denominator.

$(\frac{4 a \cdot 4 - a \cdot 5}{20} + \frac{3}{2}) \cdot 10 = \frac{7 a}{10} \cdot 10$

Simplify each term.

Simplify the numerator.

Factor $a$ out of $4 a \cdot 4 - a \cdot 5$ .

Factor $a$ out of $4 a \cdot 4$ .

$(\frac{a (4 \cdot 4) - a \cdot 5}{20} + \frac{3}{2}) \cdot 10 = \frac{7 a}{10} \cdot 10$

Factor $a$ out of $- a \cdot 5$ .

$(\frac{a (4 \cdot 4) + a (- 1 \cdot 5)}{20} + \frac{3}{2}) \cdot 10 = \frac{7 a}{10} \cdot 10$

Factor $a$ out of $a (4 \cdot 4) + a (- 1 \cdot 5)$ .

$(\frac{a (4 \cdot 4 - 1 \cdot 5)}{20} + \frac{3}{2}) \cdot 10 = \frac{7 a}{10} \cdot 10$

Multiply $4$ by $4$ .

$(\frac{a (16 - 1 \cdot 5)}{20} + \frac{3}{2}) \cdot 10 = \frac{7 a}{10} \cdot 10$

Multiply $- 1$ by $5$ .

$(\frac{a (16 - 5)}{20} + \frac{3}{2}) \cdot 10 = \frac{7 a}{10} \cdot 10$

Subtract $5$ from $16$ .

$(\frac{a \cdot 11}{20} + \frac{3}{2}) \cdot 10 = \frac{7 a}{10} \cdot 10$

Move $11$ to the left of $a$ .

$(\frac{11 a}{20} + \frac{3}{2}) \cdot 10 = \frac{7 a}{10} \cdot 10$

Simplify terms.

Apply the distributive property.

$\frac{11 a}{20} \cdot 10 + \frac{3}{2} \cdot 10 = \frac{7 a}{10} \cdot 10$

Cancel the common factor of $10$ .

Factor $10$ out of $20$ .

$\frac{11 a}{10 (2)} \cdot 10 + \frac{3}{2} \cdot 10 = \frac{7 a}{10} \cdot 10$

Cancel the common factor.

$\frac{11 a}{10 \cdot 2} \cdot 10 + \frac{3}{2} \cdot 10 = \frac{7 a}{10} \cdot 10$

Rewrite the expression.

$\frac{11 a}{2} + \frac{3}{2} \cdot 10 = \frac{7 a}{10} \cdot 10$

Cancel the common factor of $2$ .

Factor $2$ out of $10$ .

$\frac{11 a}{2} + \frac{3}{2} \cdot (2 (5)) = \frac{7 a}{10} \cdot 10$

Cancel the common factor.

$\frac{11 a}{2} + \frac{3}{2} \cdot (2 \cdot 5) = \frac{7 a}{10} \cdot 10$

Rewrite the expression.

$\frac{11 a}{2} + 3 \cdot 5 = \frac{7 a}{10} \cdot 10$

Multiply $3$ by $5$ .

$\frac{11 a}{2} + 15 = \frac{7 a}{10} \cdot 10$

Simplify the right side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{11 a}{2} + 15 = \frac{7 a}{10} \cdot 10$

Rewrite the expression.

$\frac{11 a}{2} + 15 = 7 a$

Step 3

Solve for $a$ .

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

Subtract $7 a$ from both sides of the equation.

$\frac{11 a}{2} + 15 - 7 a = 0$

To write $- 7 a$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{11 a}{2} - 7 a \cdot \frac{2}{2} + 15 = 0$

Combine $- 7 a$ and $\frac{2}{2}$ .

$\frac{11 a}{2} + \frac{- 7 a \cdot 2}{2} + 15 = 0$

Combine the numerators over the common denominator.

$\frac{11 a - 7 a \cdot 2}{2} + 15 = 0$

Simplify each term.

Simplify the numerator.

Factor $a$ out of $11 a - 7 a \cdot 2$ .

Factor $a$ out of $11 a$ .

$\frac{a \cdot 11 - 7 a \cdot 2}{2} + 15 = 0$

Factor $a$ out of $- 7 a \cdot 2$ .

$\frac{a \cdot 11 + a (- 7 \cdot 2)}{2} + 15 = 0$

Factor $a$ out of $a \cdot 11 + a (- 7 \cdot 2)$ .

$\frac{a (11 - 7 \cdot 2)}{2} + 15 = 0$

Multiply $- 7$ by $2$ .

$\frac{a (11 - 14)}{2} + 15 = 0$

Subtract $14$ from $11$ .

$\frac{a \cdot - 3}{2} + 15 = 0$

Move $- 3$ to the left of $a$ .

$\frac{- 3 \cdot a}{2} + 15 = 0$

Move the negative in front of the fraction.

$- \frac{3 a}{2} + 15 = 0$

Subtract $15$ from both sides of the equation.

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

Multiply both sides of the equation by $- \frac{2}{3}$ .

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

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

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

Move the leading negative in $- \frac{3 a}{2}$ into the numerator.

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

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

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

Multiply $a$ by $1$ .

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

Simplify the right side.

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

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

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

Factor $3$ out of $- 15$ .

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

Cancel the common factor.

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

Rewrite the expression.

$a = - 2 \cdot - 5$

Multiply $- 2$ by $- 5$ .

$a = 10$

Evaluate (4a)/5+3/2-a/4=(7a)/10

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