Algebra Examples

$6 (\frac{2}{3} a - 4) - 8 (3 + \frac{1}{2} a) = - a$

Step 1

Simplify $6 (\frac{2}{3} a - 4) - 8 (3 + \frac{1}{2} a)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{2}{3}$ and $a$ .

$6 (\frac{2 a}{3} - 4) - 8 (3 + \frac{1}{2} a) = - a$

Step 1.1.2

Apply the distributive property.

$6 \frac{2 a}{3} + 6 \cdot - 4 - 8 (3 + \frac{1}{2} a) = - a$

Step 1.1.3

Cancel the common factor of $3$ .

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Step 1.1.3.1

Factor $3$ out of $6$ .

$3 (2) \frac{2 a}{3} + 6 \cdot - 4 - 8 (3 + \frac{1}{2} a) = - a$

Step 1.1.3.2

Cancel the common factor.

$3 \cdot 2 \frac{2 a}{3} + 6 \cdot - 4 - 8 (3 + \frac{1}{2} a) = - a$

Step 1.1.3.3

Rewrite the expression.

$2 (2 a) + 6 \cdot - 4 - 8 (3 + \frac{1}{2} a) = - a$

Step 1.1.4

Multiply $2$ by $2$ .

$4 a + 6 \cdot - 4 - 8 (3 + \frac{1}{2} a) = - a$

Step 1.1.5

Multiply $6$ by $- 4$ .

$4 a - 24 - 8 (3 + \frac{1}{2} a) = - a$

Step 1.1.6

Combine $\frac{1}{2}$ and $a$ .

$4 a - 24 - 8 (3 + \frac{a}{2}) = - a$

Step 1.1.7

Apply the distributive property.

$4 a - 24 - 8 \cdot 3 - 8 \frac{a}{2} = - a$

Step 1.1.8

Multiply $- 8$ by $3$ .

$4 a - 24 - 24 - 8 \frac{a}{2} = - a$

Step 1.1.9

Cancel the common factor of $2$ .

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Step 1.1.9.1

Factor $2$ out of $- 8$ .

$4 a - 24 - 24 + 2 (- 4) \frac{a}{2} = - a$

Step 1.1.9.2

Cancel the common factor.

$4 a - 24 - 24 + 2 \cdot - 4 \frac{a}{2} = - a$

Step 1.1.9.3

Rewrite the expression.

$4 a - 24 - 24 - 4 a = - a$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Combine the opposite terms in $4 a - 24 - 24 - 4 a$ .

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Step 1.2.1.1

Subtract $4 a$ from $4 a$ .

$0 - 24 - 24 = - a$

Step 1.2.1.2

Subtract $24$ from $0$ .

$- 24 - 24 = - a$

Step 1.2.2

Subtract $24$ from $- 24$ .

$- 48 = - a$

Step 2

Since $a$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- a = - 48$

Step 3

Divide each term in $- a = - 48$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- a = - 48$ by $- 1$ .

$\frac{- a}{- 1} = \frac{- 48}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{a}{1} = \frac{- 48}{- 1}$

Step 3.2.2

Divide $a$ by $1$ .

$a = \frac{- 48}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $- 48$ by $- 1$ .

$a = 48$