Basic Math Examples

$2 l + (\frac{1}{2} l - 3) = 36$

Step 1

Simplify $2 l + \frac{1}{2} l - 3$ .

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Step 1.1

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

$2 l + \frac{l}{2} - 3 = 36$

Step 1.2

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

$2 l \cdot \frac{2}{2} + \frac{l}{2} - 3 = 36$

Step 1.3

Simplify terms.

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Step 1.3.1

Combine $2 l$ and $\frac{2}{2}$ .

$\frac{2 l \cdot 2}{2} + \frac{l}{2} - 3 = 36$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{2 l \cdot 2 + l}{2} - 3 = 36$

Step 1.4

Simplify each term.

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Step 1.4.1

Simplify the numerator.

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Step 1.4.1.1

Factor $l$ out of $2 l \cdot 2 + l$ .

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Step 1.4.1.1.1

Factor $l$ out of $2 l \cdot 2$ .

$\frac{l (2 \cdot 2) + l}{2} - 3 = 36$

Step 1.4.1.1.2

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

$\frac{l (2 \cdot 2) + l^{1}}{2} - 3 = 36$

Step 1.4.1.1.3

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

$\frac{l (2 \cdot 2) + l \cdot 1}{2} - 3 = 36$

Step 1.4.1.1.4

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

$\frac{l (2 \cdot 2 + 1)}{2} - 3 = 36$

Step 1.4.1.2

Multiply $2$ by $2$ .

$\frac{l (4 + 1)}{2} - 3 = 36$

Step 1.4.1.3

Add $4$ and $1$ .

$\frac{l \cdot 5}{2} - 3 = 36$

Step 1.4.2

Move $5$ to the left of $l$ .

$\frac{5 l}{2} - 3 = 36$

Step 2

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

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Step 2.1

Add $3$ to both sides of the equation.

$\frac{5 l}{2} = 36 + 3$

Step 2.2

Add $36$ and $3$ .

$\frac{5 l}{2} = 39$

Step 3

Multiply both sides of the equation by $\frac{2}{5}$ .

$\frac{2}{5} \cdot \frac{5 l}{2} = \frac{2}{5} \cdot 39$

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 $\frac{2}{5} \cdot \frac{5 l}{2}$ .

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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

Cancel the common factor.

$\frac{2}{5} \cdot \frac{5 l}{2} = \frac{2}{5} \cdot 39$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 l) = \frac{2}{5} \cdot 39$

Step 4.1.1.2

Cancel the common factor of $5$ .

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Step 4.1.1.2.1

Factor $5$ out of $5 l$ .

$\frac{1}{5} (5 (l)) = \frac{2}{5} \cdot 39$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 l) = \frac{2}{5} \cdot 39$

Step 4.1.1.2.3

Rewrite the expression.

$l = \frac{2}{5} \cdot 39$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $\frac{2}{5} \cdot 39$ .

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Step 4.2.1.1

Combine $\frac{2}{5}$ and $39$ .

$l = \frac{2 \cdot 39}{5}$

Step 4.2.1.2

Multiply $2$ by $39$ .

$l = \frac{78}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$l = \frac{78}{5}$

Decimal Form:

$l = 15.6$

Mixed Number Form:

$l = 15 \frac{3}{5}$