Basic Math Examples

$\frac{6 a - (a - 8)}{6} = \frac{- 2 a - 17}{3} + a$

Step 1

Multiply both sides by $6$ .

$\frac{6 a - (a - 8)}{6} \cdot 6 = (\frac{- 2 a - 17}{3} + a) \cdot 6$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{6 a - (a - 8)}{6} \cdot 6$ .

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Step 2.1.1.1

Simplify the numerator.

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Step 2.1.1.1.1

Apply the distributive property.

$\frac{6 a - a - - 8}{6} \cdot 6 = (\frac{- 2 a - 17}{3} + a) \cdot 6$

Step 2.1.1.1.2

Multiply $- 1$ by $- 8$ .

$\frac{6 a - a + 8}{6} \cdot 6 = (\frac{- 2 a - 17}{3} + a) \cdot 6$

Step 2.1.1.1.3

Subtract $a$ from $6 a$ .

$\frac{5 a + 8}{6} \cdot 6 = (\frac{- 2 a - 17}{3} + a) \cdot 6$

Step 2.1.1.2

Cancel the common factor of $6$ .

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Step 2.1.1.2.1

Cancel the common factor.

$\frac{5 a + 8}{6} \cdot 6 = (\frac{- 2 a - 17}{3} + a) \cdot 6$

Step 2.1.1.2.2

Rewrite the expression.

$5 a + 8 = (\frac{- 2 a - 17}{3} + a) \cdot 6$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(\frac{- 2 a - 17}{3} + a) \cdot 6$ .

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Step 2.2.1.1

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

$5 a + 8 = (\frac{- 2 a - 17}{3} + a \cdot \frac{3}{3}) \cdot 6$

Step 2.2.1.2

Simplify terms.

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Step 2.2.1.2.1

Combine $a$ and $\frac{3}{3}$ .

$5 a + 8 = (\frac{- 2 a - 17}{3} + \frac{a \cdot 3}{3}) \cdot 6$

Step 2.2.1.2.2

Combine the numerators over the common denominator.

$5 a + 8 = \frac{- 2 a - 17 + a \cdot 3}{3} \cdot 6$

Step 2.2.1.3

Simplify the numerator.

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Step 2.2.1.3.1

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

$5 a + 8 = \frac{- 2 a - 17 + 3 \cdot a}{3} \cdot 6$

Step 2.2.1.3.2

Add $- 2 a$ and $3 a$ .

$5 a + 8 = \frac{a - 17}{3} \cdot 6$

Step 2.2.1.4

Simplify terms.

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Step 2.2.1.4.1

Cancel the common factor of $3$ .

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Step 2.2.1.4.1.1

Factor $3$ out of $6$ .

$5 a + 8 = \frac{a - 17}{3} \cdot (3 (2))$

Step 2.2.1.4.1.2

Cancel the common factor.

$5 a + 8 = \frac{a - 17}{3} \cdot (3 \cdot 2)$

Step 2.2.1.4.1.3

Rewrite the expression.

$5 a + 8 = (a - 17) \cdot 2$

Step 2.2.1.4.2

Apply the distributive property.

$5 a + 8 = a \cdot 2 - 17 \cdot 2$

Step 2.2.1.4.3

Simplify the expression.

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Step 2.2.1.4.3.1

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

$5 a + 8 = 2 \cdot a - 17 \cdot 2$

Step 2.2.1.4.3.2

Multiply $- 17$ by $2$ .

$5 a + 8 = 2 a - 34$

Step 3

Solve for $a$ .

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Step 3.1

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

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Step 3.1.1

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

$5 a + 8 - 2 a = - 34$

Step 3.1.2

Subtract $2 a$ from $5 a$ .

$3 a + 8 = - 34$

Step 3.2

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

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Step 3.2.1

Subtract $8$ from both sides of the equation.

$3 a = - 34 - 8$

Step 3.2.2

Subtract $8$ from $- 34$ .

$3 a = - 42$

Step 3.3

Divide each term in $3 a = - 42$ by $3$ and simplify.

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Step 3.3.1

Divide each term in $3 a = - 42$ by $3$ .

$\frac{3 a}{3} = \frac{- 42}{3}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $3$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{3 a}{3} = \frac{- 42}{3}$

Step 3.3.2.1.2

Divide $a$ by $1$ .

$a = \frac{- 42}{3}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $- 42$ by $3$ .

$a = - 14$