Basic Math Examples

$\frac{b}{2} + 5 = 2 b$

Step 1

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

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Step 1.1

Subtract $2 b$ from both sides of the equation.

$\frac{b}{2} + 5 - 2 b = 0$

Step 1.2

To write $- 2 b$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{b}{2} - 2 b \cdot \frac{2}{2} + 5 = 0$

Step 1.3

Combine $- 2 b$ and $\frac{2}{2}$ .

$\frac{b}{2} + \frac{- 2 b \cdot 2}{2} + 5 = 0$

Step 1.4

Combine the numerators over the common denominator.

$\frac{b - 2 b \cdot 2}{2} + 5 = 0$

Step 1.5

Simplify each term.

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Step 1.5.1

Simplify the numerator.

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Step 1.5.1.1

Factor $b$ out of $b - 2 b \cdot 2$ .

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Step 1.5.1.1.1

Raise $b$ to the power of $1$ .

$\frac{b^{1} - 2 b \cdot 2}{2} + 5 = 0$

Step 1.5.1.1.2

Factor $b$ out of $b^{1}$ .

$\frac{b \cdot 1 - 2 b \cdot 2}{2} + 5 = 0$

Step 1.5.1.1.3

Factor $b$ out of $- 2 b \cdot 2$ .

$\frac{b \cdot 1 + b (- 2 \cdot 2)}{2} + 5 = 0$

Step 1.5.1.1.4

Factor $b$ out of $b \cdot 1 + b (- 2 \cdot 2)$ .

$\frac{b (1 - 2 \cdot 2)}{2} + 5 = 0$

Step 1.5.1.2

Multiply $- 2$ by $2$ .

$\frac{b (1 - 4)}{2} + 5 = 0$

Step 1.5.1.3

Subtract $4$ from $1$ .

$\frac{b \cdot - 3}{2} + 5 = 0$

Step 1.5.2

Move $- 3$ to the left of $b$ .

$\frac{- 3 \cdot b}{2} + 5 = 0$

Step 1.5.3

Move the negative in front of the fraction.

$- \frac{3 b}{2} + 5 = 0$

Step 2

Subtract $5$ from both sides of the equation.

$- \frac{3 b}{2} = - 5$

Step 3

Multiply both sides of the equation by $- \frac{2}{3}$ .

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

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 $- \frac{2}{3} (- \frac{3 b}{2})$ .

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Step 4.1.1.1

Cancel the common factor of $2$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

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

Step 4.1.1.1.2

Move the leading negative in $- \frac{3 b}{2}$ into the numerator.

$\frac{- 2}{3} \cdot \frac{- 3 b}{2} = - \frac{2}{3} \cdot - 5$

Step 4.1.1.1.3

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{3} \cdot \frac{- 3 b}{2} = - \frac{2}{3} \cdot - 5$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{2 \cdot - 1}{3} \cdot \frac{- 3 b}{2} = - \frac{2}{3} \cdot - 5$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{3} (- 3 b) = - \frac{2}{3} \cdot - 5$

Step 4.1.1.2

Cancel the common factor of $3$ .

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Step 4.1.1.2.1

Factor $3$ out of $- 3 b$ .

$\frac{- 1}{3} (3 (- b)) = - \frac{2}{3} \cdot - 5$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{3} (3 (- b)) = - \frac{2}{3} \cdot - 5$

Step 4.1.1.2.3

Rewrite the expression.

$- - b = - \frac{2}{3} \cdot - 5$

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 b = - \frac{2}{3} \cdot - 5$

Step 4.1.1.3.2

Multiply $b$ by $1$ .

$b = - \frac{2}{3} \cdot - 5$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- \frac{2}{3} \cdot - 5$ .

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Step 4.2.1.1

Multiply $- 5$ by $- 1$ .

$b = 5 (\frac{2}{3})$

Step 4.2.1.2

Combine $5$ and $\frac{2}{3}$ .

$b = \frac{5 \cdot 2}{3}$

Step 4.2.1.3

Multiply $5$ by $2$ .

$b = \frac{10}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$b = \frac{10}{3}$

Decimal Form:

$b = 3.\overline{3}$

Mixed Number Form:

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