Algebra Examples

$- 4 (5 - 2 a) + 3 (a - 4) = 6 (2 - a) - 5 a$

Step 1

Simplify $- 4 (5 - 2 a) + 3 (a - 4)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$- 4 \cdot 5 - 4 (- 2 a) + 3 (a - 4) = 6 (2 - a) - 5 a$

Step 1.1.2

Multiply $- 4$ by $5$ .

$- 20 - 4 (- 2 a) + 3 (a - 4) = 6 (2 - a) - 5 a$

Step 1.1.3

Multiply $- 2$ by $- 4$ .

$- 20 + 8 a + 3 (a - 4) = 6 (2 - a) - 5 a$

Step 1.1.4

Apply the distributive property.

$- 20 + 8 a + 3 a + 3 \cdot - 4 = 6 (2 - a) - 5 a$

Step 1.1.5

Multiply $3$ by $- 4$ .

$- 20 + 8 a + 3 a - 12 = 6 (2 - a) - 5 a$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Subtract $12$ from $- 20$ .

$8 a + 3 a - 32 = 6 (2 - a) - 5 a$

Step 1.2.2

Add $8 a$ and $3 a$ .

$11 a - 32 = 6 (2 - a) - 5 a$

Step 2

Simplify $6 (2 - a) - 5 a$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$11 a - 32 = 6 \cdot 2 + 6 (- a) - 5 a$

Step 2.1.2

Multiply $6$ by $2$ .

$11 a - 32 = 12 + 6 (- a) - 5 a$

Step 2.1.3

Multiply $- 1$ by $6$ .

$11 a - 32 = 12 - 6 a - 5 a$

Step 2.2

Subtract $5 a$ from $- 6 a$ .

$11 a - 32 = 12 - 11 a$

Step 3

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

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Step 3.1

Add $11 a$ to both sides of the equation.

$11 a - 32 + 11 a = 12$

Step 3.2

Add $11 a$ and $11 a$ .

$22 a - 32 = 12$

Step 4

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

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Step 4.1

Add $32$ to both sides of the equation.

$22 a = 12 + 32$

Step 4.2

Add $12$ and $32$ .

$22 a = 44$

Step 5

Divide each term in $22 a = 44$ by $22$ and simplify.

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Step 5.1

Divide each term in $22 a = 44$ by $22$ .

$\frac{22 a}{22} = \frac{44}{22}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $22$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{22 a}{22} = \frac{44}{22}$

Step 5.2.1.2

Divide $a$ by $1$ .

$a = \frac{44}{22}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $44$ by $22$ .

$a = 2$