Algebra Examples

$\frac{a}{6} - 10 = \frac{a}{3}$

Step 1

Multiply each term in $\frac{a}{6} - 10 = \frac{a}{3}$ by $6$ to eliminate the fractions.

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Step 1.1

Multiply each term in $\frac{a}{6} - 10 = \frac{a}{3}$ by $6$ .

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

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Cancel the common factor of $6$ .

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Step 1.2.1.1.1

Cancel the common factor.

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

Step 1.2.1.1.2

Rewrite the expression.

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

Step 1.2.1.2

Multiply $- 10$ by $6$ .

$a - 60 = \frac{a}{3} \cdot 6$

Step 1.3

Simplify the right side.

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Step 1.3.1

Cancel the common factor of $3$ .

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Step 1.3.1.1

Factor $3$ out of $6$ .

$a - 60 = \frac{a}{3} \cdot (3 (2))$

Step 1.3.1.2

Cancel the common factor.

$a - 60 = \frac{a}{3} \cdot (3 \cdot 2)$

Step 1.3.1.3

Rewrite the expression.

$a - 60 = a \cdot 2$

Step 1.3.2

Move $2$ to the left of $a$ .

$a - 60 = 2 a$

Step 2

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

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Step 2.1

Subtract $2 a$ from both sides of the equation.

$a - 60 - 2 a = 0$

Step 2.2

Subtract $2 a$ from $a$ .

$- a - 60 = 0$

Step 3

Add $60$ to both sides of the equation.

$- a = 60$

Step 4

Divide each term in $- a = 60$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- a = 60$ by $- 1$ .

$\frac{- a}{- 1} = \frac{60}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{a}{1} = \frac{60}{- 1}$

Step 4.2.2

Divide $a$ by $1$ .

$a = \frac{60}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $60$ by $- 1$ .

$a = - 60$