Basic Math Examples

$240 = \frac{1}{2} \cdot (34 + b) \cdot 12$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot (34 + b) \cdot 12 = 240$ .

$\frac{1}{2} \cdot (34 + b) \cdot 12 = 240$

Step 2

Simplify.

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Step 2.1

Apply the distributive property.

$(\frac{1}{2} \cdot 34 + \frac{1}{2} b) \cdot 12 = 240$

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Factor $2$ out of $34$ .

$(\frac{1}{2} \cdot (2 (17)) + \frac{1}{2} b) \cdot 12 = 240$

Step 2.2.2

Cancel the common factor.

$(\frac{1}{2} \cdot (2 \cdot 17) + \frac{1}{2} b) \cdot 12 = 240$

Step 2.2.3

Rewrite the expression.

$(17 + \frac{1}{2} b) \cdot 12 = 240$

Step 2.3

Combine $\frac{1}{2}$ and $b$ .

$(17 + \frac{b}{2}) \cdot 12 = 240$

Step 3

Divide each term in $(17 + \frac{b}{2}) \cdot 12 = 240$ by $12$ and simplify.

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Step 3.1

Divide each term in $(17 + \frac{b}{2}) \cdot 12 = 240$ by $12$ .

$\frac{(17 + \frac{b}{2}) \cdot 12}{12} = \frac{240}{12}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $12$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{(17 + \frac{b}{2}) \cdot 12}{12} = \frac{240}{12}$

Step 3.2.1.2

Divide $17 + \frac{b}{2}$ by $1$ .

$17 + \frac{b}{2} = \frac{240}{12}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $240$ by $12$ .

$17 + \frac{b}{2} = 20$

Step 4

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

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Step 4.1

Subtract $17$ from both sides of the equation.

$\frac{b}{2} = 20 - 17$

Step 4.2

Subtract $17$ from $20$ .

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

Step 5

Multiply both sides of the equation by $2$ .

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

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Cancel the common factor of $2$ .

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Step 6.1.1.1

Cancel the common factor.

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

Step 6.1.1.2

Rewrite the expression.

$b = 2 \cdot 3$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $2$ by $3$ .

$b = 6$