Solve for a 1/6a-1/4*(a-5)=1

$\frac{1}{6} a - \frac{1}{4} \cdot (a - 5) = 1$

Step 1

Simplify $\frac{1}{6} a - \frac{1}{4} \cdot (a - 5)$ .

Simplify each term.

Combine $\frac{1}{6}$ and $a$ .

$\frac{a}{6} - \frac{1}{4} \cdot (a - 5) = 1$

Apply the distributive property.

$\frac{a}{6} - \frac{1}{4} a - \frac{1}{4} \cdot - 5 = 1$

Combine $a$ and $\frac{1}{4}$ .

$\frac{a}{6} - \frac{a}{4} - \frac{1}{4} \cdot - 5 = 1$

Multiply $- \frac{1}{4} \cdot - 5$ .

Multiply $- 5$ by $- 1$ .

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

Combine $5$ and $\frac{1}{4}$ .

$\frac{a}{6} - \frac{a}{4} + \frac{5}{4} = 1$

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

$\frac{a}{6} \cdot \frac{2}{2} - \frac{a}{4} + \frac{5}{4} = 1$

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

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

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $6$ by $2$ .

$\frac{a \cdot 2}{12} - \frac{a}{4} \cdot \frac{3}{3} + \frac{5}{4} = 1$

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

$\frac{a \cdot 2}{12} - \frac{a \cdot 3}{4 \cdot 3} + \frac{5}{4} = 1$

Multiply $4$ by $3$ .

$\frac{a \cdot 2}{12} - \frac{a \cdot 3}{12} + \frac{5}{4} = 1$

Combine the numerators over the common denominator.

$\frac{a \cdot 2 - a \cdot 3}{12} + \frac{5}{4} = 1$

Simplify each term.

Simplify the numerator.

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

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

$\frac{a (2) - a \cdot 3}{12} + \frac{5}{4} = 1$

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

$\frac{a (2) + a (- 1 \cdot 3)}{12} + \frac{5}{4} = 1$

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

$\frac{a (2 - 1 \cdot 3)}{12} + \frac{5}{4} = 1$

Multiply $- 1$ by $3$ .

$\frac{a (2 - 3)}{12} + \frac{5}{4} = 1$

Subtract $3$ from $2$ .

$\frac{a \cdot - 1}{12} + \frac{5}{4} = 1$

Move $- 1$ to the left of $a$ .

$\frac{- 1 \cdot a}{12} + \frac{5}{4} = 1$

Move the negative in front of the fraction.

$- \frac{a}{12} + \frac{5}{4} = 1$

Step 2

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

Subtract $\frac{5}{4}$ from both sides of the equation.

$- \frac{a}{12} = 1 - \frac{5}{4}$

Write $1$ as a fraction with a common denominator.

$- \frac{a}{12} = \frac{4}{4} - \frac{5}{4}$

Combine the numerators over the common denominator.

$- \frac{a}{12} = \frac{4 - 5}{4}$

Subtract $5$ from $4$ .

$- \frac{a}{12} = \frac{- 1}{4}$

Move the negative in front of the fraction.

$- \frac{a}{12} = - \frac{1}{4}$

Step 3

Multiply both sides of the equation by $- 12$ .

$- 12 (- \frac{a}{12}) = - 12 (- \frac{1}{4})$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 12 (- \frac{a}{12})$ .

Cancel the common factor of $12$ .

Move the leading negative in $- \frac{a}{12}$ into the numerator.

$- 12 \frac{- a}{12} = - 12 (- \frac{1}{4})$

Factor $12$ out of $- 12$ .

$12 (- 1) \frac{- a}{12} = - 12 (- \frac{1}{4})$

Cancel the common factor.

$12 \cdot - 1 \frac{- a}{12} = - 12 (- \frac{1}{4})$

Rewrite the expression.

$- - a = - 12 (- \frac{1}{4})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 a = - 12 (- \frac{1}{4})$

Multiply $a$ by $1$ .

$a = - 12 (- \frac{1}{4})$

Simplify the right side.

Simplify $- 12 (- \frac{1}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$a = - 12 (\frac{- 1}{4})$

Factor $4$ out of $- 12$ .

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

Cancel the common factor.

$a = 4 \cdot - 3 \frac{- 1}{4}$

Rewrite the expression.

$a = - 3 \cdot - 1$

Multiply $- 3$ by $- 1$ .

$a = 3$

Solve for a 1/6a-1/4*(a-5)=1

Related Questions