Solve for a 1/14(a+8)=1/4(3-a)

$\frac{1}{14} (a + 8) = \frac{1}{4} (3 - a)$

Simplify $\frac{1}{14} \cdot (a + 8)$ .

Start simplifying.

$0 + 0 + \frac{1}{14} \cdot (a + 8) = \frac{1}{4} \cdot (3 - a)$

Simplify by adding zeros.

$\frac{1}{14} \cdot (a + 8) = \frac{1}{4} \cdot (3 - a)$

Apply the distributive property.

$\frac{1}{14} a + \frac{1}{14} \cdot 8 = \frac{1}{4} \cdot (3 - a)$

Combine $\frac{1}{14}$ and $a$ .

$\frac{a}{14} + \frac{1}{14} \cdot 8 = \frac{1}{4} \cdot (3 - a)$

Cancel the common factor of $2$ .

Factor $2$ out of $14$ .

$\frac{a}{14} + \frac{1}{2 (7)} \cdot 8 = \frac{1}{4} \cdot (3 - a)$

Factor $2$ out of $8$ .

$\frac{a}{14} + \frac{1}{2 \cdot 7} \cdot (2 \cdot 4) = \frac{1}{4} \cdot (3 - a)$

Cancel the common factor.

$\frac{a}{14} + \frac{1}{2 \cdot 7} \cdot (2 \cdot 4) = \frac{1}{4} \cdot (3 - a)$

Rewrite the expression.

$\frac{a}{14} + \frac{1}{7} \cdot 4 = \frac{1}{4} \cdot (3 - a)$

Combine $\frac{1}{7}$ and $4$ .

$\frac{a}{14} + \frac{4}{7} = \frac{1}{4} \cdot (3 - a)$

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

Apply the distributive property.

$\frac{a}{14} + \frac{4}{7} = \frac{1}{4} \cdot 3 + \frac{1}{4} (- a)$

Combine $\frac{1}{4}$ and $3$ .

$\frac{a}{14} + \frac{4}{7} = \frac{3}{4} + \frac{1}{4} (- a)$

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

$\frac{a}{14} + \frac{4}{7} = \frac{3}{4} - \frac{a}{4}$

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

Add $\frac{a}{4}$ to both sides of the equation.

$\frac{a}{14} + \frac{4}{7} + \frac{a}{4} = \frac{3}{4}$

To write $\frac{a}{14}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{a}{14} \cdot \frac{2}{2} + \frac{a}{4} + \frac{4}{7} = \frac{3}{4}$

To write $\frac{a}{4}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{a}{14} \cdot \frac{2}{2} + \frac{a}{4} \cdot \frac{7}{7} + \frac{4}{7} = \frac{3}{4}$

Write each expression with a common denominator of $28$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{a}{14}$ by $\frac{2}{2}$ .

$\frac{a \cdot 2}{14 \cdot 2} + \frac{a}{4} \cdot \frac{7}{7} + \frac{4}{7} = \frac{3}{4}$

Multiply $14$ by $2$ .

$\frac{a \cdot 2}{28} + \frac{a}{4} \cdot \frac{7}{7} + \frac{4}{7} = \frac{3}{4}$

Multiply $\frac{a}{4}$ by $\frac{7}{7}$ .

$\frac{a \cdot 2}{28} + \frac{a \cdot 7}{4 \cdot 7} + \frac{4}{7} = \frac{3}{4}$

Multiply $4$ by $7$ .

$\frac{a \cdot 2}{28} + \frac{a \cdot 7}{28} + \frac{4}{7} = \frac{3}{4}$

Combine the numerators over the common denominator.

$\frac{a \cdot 2 + a \cdot 7}{28} + \frac{4}{7} = \frac{3}{4}$

Reorder $a$ and $7$ .

$\frac{2 \cdot a + 7 \cdot a}{28} + \frac{4}{7} = \frac{3}{4}$

Add $2 \cdot a$ and $7 \cdot a$ .

$\frac{9 a}{28} + \frac{4}{7} = \frac{3}{4}$

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

Subtract $\frac{4}{7}$ from both sides of the equation.

$\frac{9 a}{28} = \frac{3}{4} - \frac{4}{7}$

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{9 a}{28} = \frac{3}{4} \cdot \frac{7}{7} - \frac{4}{7}$

To write $- \frac{4}{7}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{9 a}{28} = \frac{3}{4} \cdot \frac{7}{7} - \frac{4}{7} \cdot \frac{4}{4}$

Write each expression with a common denominator of $28$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{4}$ by $\frac{7}{7}$ .

$\frac{9 a}{28} = \frac{3 \cdot 7}{4 \cdot 7} - \frac{4}{7} \cdot \frac{4}{4}$

Multiply $4$ by $7$ .

$\frac{9 a}{28} = \frac{3 \cdot 7}{28} - \frac{4}{7} \cdot \frac{4}{4}$

Multiply $\frac{4}{7}$ by $\frac{4}{4}$ .

$\frac{9 a}{28} = \frac{3 \cdot 7}{28} - \frac{4 \cdot 4}{7 \cdot 4}$

Multiply $7$ by $4$ .

$\frac{9 a}{28} = \frac{3 \cdot 7}{28} - \frac{4 \cdot 4}{28}$

Combine the numerators over the common denominator.

$\frac{9 a}{28} = \frac{3 \cdot 7 - 4 \cdot 4}{28}$

Simplify the numerator.

Multiply $3$ by $7$ .

$\frac{9 a}{28} = \frac{21 - 4 \cdot 4}{28}$

Multiply $- 4$ by $4$ .

$\frac{9 a}{28} = \frac{21 - 16}{28}$

Subtract $16$ from $21$ .

$\frac{9 a}{28} = \frac{5}{28}$

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

$9 a = 5$

Divide each term in $9 a = 5$ by $9$ and simplify.

Divide each term in $9 a = 5$ by $9$ .

$\frac{9 a}{9} = \frac{5}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 a}{9} = \frac{5}{9}$

Divide $a$ by $1$ .

$a = \frac{5}{9}$

The result can be shown in multiple forms.

Exact Form:

$a = \frac{5}{9}$

Decimal Form:

$a = 0.\overline{5}$

Solve for a 1/14(a+8)=1/4(3-a)

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