Basic Math Examples

$- 4 (- a + 4) + 2 (3 a + 2) = - a + 8 - 4 a$

Step 1

Simplify $- 4 (- a + 4) + 2 (3 a + 2)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$- 4 (- a) - 4 \cdot 4 + 2 (3 a + 2) = - a + 8 - 4 a$

Step 1.1.2

Multiply $- 1$ by $- 4$ .

$4 a - 4 \cdot 4 + 2 (3 a + 2) = - a + 8 - 4 a$

Step 1.1.3

Multiply $- 4$ by $4$ .

$4 a - 16 + 2 (3 a + 2) = - a + 8 - 4 a$

Step 1.1.4

Apply the distributive property.

$4 a - 16 + 2 (3 a) + 2 \cdot 2 = - a + 8 - 4 a$

Step 1.1.5

Multiply $3$ by $2$ .

$4 a - 16 + 6 a + 2 \cdot 2 = - a + 8 - 4 a$

Step 1.1.6

Multiply $2$ by $2$ .

$4 a - 16 + 6 a + 4 = - a + 8 - 4 a$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Add $4 a$ and $6 a$ .

$10 a - 16 + 4 = - a + 8 - 4 a$

Step 1.2.2

Add $- 16$ and $4$ .

$10 a - 12 = - a + 8 - 4 a$

Step 2

Subtract $4 a$ from $- a$ .

$10 a - 12 = - 5 a + 8$

Step 3

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

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Step 3.1

Add $5 a$ to both sides of the equation.

$10 a - 12 + 5 a = 8$

Step 3.2

Add $10 a$ and $5 a$ .

$15 a - 12 = 8$

Step 4

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

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Step 4.1

Add $12$ to both sides of the equation.

$15 a = 8 + 12$

Step 4.2

Add $8$ and $12$ .

$15 a = 20$

Step 5

Divide each term in $15 a = 20$ by $15$ and simplify.

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Step 5.1

Divide each term in $15 a = 20$ by $15$ .

$\frac{15 a}{15} = \frac{20}{15}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $15$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{15 a}{15} = \frac{20}{15}$

Step 5.2.1.2

Divide $a$ by $1$ .

$a = \frac{20}{15}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $20$ and $15$ .

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Step 5.3.1.1

Factor $5$ out of $20$ .

$a = \frac{5 (4)}{15}$

Step 5.3.1.2

Cancel the common factors.

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Step 5.3.1.2.1

Factor $5$ out of $15$ .

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

Step 5.3.1.2.2

Cancel the common factor.

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

Step 5.3.1.2.3

Rewrite the expression.

$a = \frac{4}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$a = \frac{4}{3}$

Decimal Form:

$a = 1.\overline{3}$

Mixed Number Form:

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