Algebra Examples

$4 (a + 3) - 2 (a + 6) = 20$

Step 1

Simplify $4 (a + 3) - 2 (a + 6)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$4 a + 4 \cdot 3 - 2 (a + 6) = 20$

Step 1.1.2

Multiply $4$ by $3$ .

$4 a + 12 - 2 (a + 6) = 20$

Step 1.1.3

Apply the distributive property.

$4 a + 12 - 2 a - 2 \cdot 6 = 20$

Step 1.1.4

Multiply $- 2$ by $6$ .

$4 a + 12 - 2 a - 12 = 20$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Combine the opposite terms in $4 a + 12 - 2 a - 12$ .

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Step 1.2.1.1

Subtract $12$ from $12$ .

$4 a - 2 a + 0 = 20$

Step 1.2.1.2

Add $4 a - 2 a$ and $0$ .

$4 a - 2 a = 20$

Step 1.2.2

Subtract $2 a$ from $4 a$ .

$2 a = 20$

Step 2

Divide each term in $2 a = 20$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 a = 20$ by $2$ .

$\frac{2 a}{2} = \frac{20}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 a}{2} = \frac{20}{2}$

Step 2.2.1.2

Divide $a$ by $1$ .

$a = \frac{20}{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $20$ by $2$ .

$a = 10$