Basic Math Examples

$\frac{- 3 a - 6}{2} = 4 - 5 a$

Step 1

Multiply both sides by $2$ .

$\frac{- 3 a - 6}{2} \cdot 2 = (4 - 5 a) \cdot 2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{- 3 a - 6}{2} \cdot 2$ .

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Step 2.1.1.1

Factor $3$ out of $- 3 a - 6$ .

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Step 2.1.1.1.1

Factor $3$ out of $- 3 a$ .

$\frac{3 (- a) - 6}{2} \cdot 2 = (4 - 5 a) \cdot 2$

Step 2.1.1.1.2

Factor $3$ out of $- 6$ .

$\frac{3 (- a) + 3 (- 2)}{2} \cdot 2 = (4 - 5 a) \cdot 2$

Step 2.1.1.1.3

Factor $3$ out of $3 (- a) + 3 (- 2)$ .

$\frac{3 (- a - 2)}{2} \cdot 2 = (4 - 5 a) \cdot 2$

Step 2.1.1.2

Cancel the common factor of $2$ .

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Step 2.1.1.2.1

Cancel the common factor.

$\frac{3 (- a - 2)}{2} \cdot 2 = (4 - 5 a) \cdot 2$

Step 2.1.1.2.2

Rewrite the expression.

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

Step 2.1.1.3

Apply the distributive property.

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

Step 2.1.1.4

Multiply.

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Step 2.1.1.4.1

Multiply $- 1$ by $3$ .

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

Step 2.1.1.4.2

Multiply $3$ by $- 2$ .

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

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(4 - 5 a) \cdot 2$ .

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Step 2.2.1.1

Apply the distributive property.

$- 3 a - 6 = 4 \cdot 2 - 5 a \cdot 2$

Step 2.2.1.2

Simplify the expression.

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Step 2.2.1.2.1

Multiply $4$ by $2$ .

$- 3 a - 6 = 8 - 5 a \cdot 2$

Step 2.2.1.2.2

Multiply $2$ by $- 5$ .

$- 3 a - 6 = 8 - 10 a$

Step 2.2.1.2.3

Reorder $8$ and $- 10 a$ .

$- 3 a - 6 = - 10 a + 8$

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

Add $10 a$ to both sides of the equation.

$- 3 a - 6 + 10 a = 8$

Step 3.1.2

Add $- 3 a$ and $10 a$ .

$7 a - 6 = 8$

Step 3.2

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

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Step 3.2.1

Add $6$ to both sides of the equation.

$7 a = 8 + 6$

Step 3.2.2

Add $8$ and $6$ .

$7 a = 14$

Step 3.3

Divide each term in $7 a = 14$ by $7$ and simplify.

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Step 3.3.1

Divide each term in $7 a = 14$ by $7$ .

$\frac{7 a}{7} = \frac{14}{7}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $7$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{7 a}{7} = \frac{14}{7}$

Step 3.3.2.1.2

Divide $a$ by $1$ .

$a = \frac{14}{7}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $14$ by $7$ .

$a = 2$