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

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

Step 1

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

Rewrite.

$0 + 0 + \frac{1}{4} \cdot (a + 2) = \frac{1}{6} \cdot (5 - a)$

Simplify by adding zeros.

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

Apply the distributive property.

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

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

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

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

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

Apply the distributive property.

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

Combine $\frac{1}{6}$ and $5$ .

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

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

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

Step 3

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

Add $\frac{a}{6}$ to both sides of the equation.

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

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

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

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

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

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

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

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

Multiply $4$ by $3$ .

$\frac{a \cdot 3}{12} + \frac{a}{6} \cdot \frac{2}{2} + \frac{1}{2} = \frac{5}{6}$

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

$\frac{a \cdot 3}{12} + \frac{a \cdot 2}{6 \cdot 2} + \frac{1}{2} = \frac{5}{6}$

Multiply $6$ by $2$ .

$\frac{a \cdot 3}{12} + \frac{a \cdot 2}{12} + \frac{1}{2} = \frac{5}{6}$

Combine the numerators over the common denominator.

$\frac{a \cdot 3 + a \cdot 2}{12} + \frac{1}{2} = \frac{5}{6}$

Reorder $a$ and $2$ .

$\frac{3 \cdot a + 2 \cdot a}{12} + \frac{1}{2} = \frac{5}{6}$

Add $3 \cdot a$ and $2 \cdot a$ .

$\frac{5 a}{12} + \frac{1}{2} = \frac{5}{6}$

Step 4

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

Subtract $\frac{1}{2}$ from both sides of the equation.

$\frac{5 a}{12} = \frac{5}{6} - \frac{1}{2}$

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

$\frac{5 a}{12} = \frac{5}{6} - \frac{1}{2} \cdot \frac{3}{3}$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$\frac{5 a}{12} = \frac{5}{6} - \frac{3}{2 \cdot 3}$

Multiply $2$ by $3$ .

$\frac{5 a}{12} = \frac{5}{6} - \frac{3}{6}$

Combine the numerators over the common denominator.

$\frac{5 a}{12} = \frac{5 - 3}{6}$

Subtract $3$ from $5$ .

$\frac{5 a}{12} = \frac{2}{6}$

Cancel the common factor of $2$ and $6$ .

Factor $2$ out of $2$ .

$\frac{5 a}{12} = \frac{2 (1)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{5 a}{12} = \frac{1}{3}$

Step 5

Multiply both sides of the equation by $\frac{12}{5}$ .

$\frac{12}{5} \cdot \frac{5 a}{12} = \frac{12}{5} \cdot \frac{1}{3}$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{12}{5} \cdot \frac{5 a}{12}$ .

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12}{5} \cdot \frac{5 a}{12} = \frac{12}{5} \cdot \frac{1}{3}$

Rewrite the expression.

$\frac{1}{5} (5 a) = \frac{12}{5} \cdot \frac{1}{3}$

Cancel the common factor of $5$ .

Factor $5$ out of $5 a$ .

$\frac{1}{5} (5 (a)) = \frac{12}{5} \cdot \frac{1}{3}$

Cancel the common factor.

$\frac{1}{5} (5 a) = \frac{12}{5} \cdot \frac{1}{3}$

Rewrite the expression.

$a = \frac{12}{5} \cdot \frac{1}{3}$

Simplify the right side.

Cancel the common factor of $3$ .

Factor $3$ out of $12$ .

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

Cancel the common factor.

$a = \frac{3 \cdot 4}{5} \cdot \frac{1}{3}$

Rewrite the expression.

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$a = 0.8$

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

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