Pre-Algebra Examples

$\frac{b}{3} + 5 = - b - 3$

Step 1

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

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Step 1.1

Add $b$ to both sides of the equation.

$\frac{b}{3} + 5 + b = - 3$

Step 1.2

To write $b$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{b}{3} + b \cdot \frac{3}{3} + 5 = - 3$

Step 1.3

Combine $b$ and $\frac{3}{3}$ .

$\frac{b}{3} + \frac{b \cdot 3}{3} + 5 = - 3$

Step 1.4

Combine the numerators over the common denominator.

$\frac{b + b \cdot 3}{3} + 5 = - 3$

Step 1.5

Add $b$ and $b \cdot 3$ .

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Step 1.5.1

Reorder $b$ and $3$ .

$\frac{b + 3 \cdot b}{3} + 5 = - 3$

Step 1.5.2

Add $b$ and $3 \cdot b$ .

$\frac{4 b}{3} + 5 = - 3$

Step 2

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

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Step 2.1

Subtract $5$ from both sides of the equation.

$\frac{4 b}{3} = - 3 - 5$

Step 2.2

Subtract $5$ from $- 3$ .

$\frac{4 b}{3} = - 8$

Step 3

Multiply both sides of the equation by $\frac{3}{4}$ .

$\frac{3}{4} \cdot \frac{4 b}{3} = \frac{3}{4} \cdot - 8$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{3}{4} \cdot \frac{4 b}{3}$ .

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Step 4.1.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{3}{4} \cdot \frac{4 b}{3} = \frac{3}{4} \cdot - 8$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{4} (4 b) = \frac{3}{4} \cdot - 8$

Step 4.1.1.2

Cancel the common factor of $4$ .

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Step 4.1.1.2.1

Factor $4$ out of $4 b$ .

$\frac{1}{4} (4 (b)) = \frac{3}{4} \cdot - 8$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{4} (4 b) = \frac{3}{4} \cdot - 8$

Step 4.1.1.2.3

Rewrite the expression.

$b = \frac{3}{4} \cdot - 8$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{3}{4} \cdot - 8$ .

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Step 4.2.1.1

Cancel the common factor of $4$ .

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Step 4.2.1.1.1

Factor $4$ out of $- 8$ .

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

Step 4.2.1.1.2

Cancel the common factor.

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

Step 4.2.1.1.3

Rewrite the expression.

$b = 3 \cdot - 2$

Step 4.2.1.2

Multiply $3$ by $- 2$ .

$b = - 6$