Algebra Examples

$2 \frac{1}{2} x - \frac{3}{4} (2 x + 5) = \frac{3}{8}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $2 \frac{1}{2} x - \frac{3}{4} \cdot (2 x + 5)$ .

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Step 1.1.1

Convert $2 \frac{1}{2}$ to an improper fraction.

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Step 1.1.1.1

A mixed number is an addition of its whole and fractional parts.

$(2 + \frac{1}{2}) x - \frac{3}{4} \cdot (2 x + 5) = \frac{3}{8}$

Step 1.1.1.2

Add $2$ and $\frac{1}{2}$ .

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Step 1.1.1.2.1

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

$(2 \cdot \frac{2}{2} + \frac{1}{2}) x - \frac{3}{4} \cdot (2 x + 5) = \frac{3}{8}$

Step 1.1.1.2.2

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

$(\frac{2 \cdot 2}{2} + \frac{1}{2}) x - \frac{3}{4} \cdot (2 x + 5) = \frac{3}{8}$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 2 + 1}{2} x - \frac{3}{4} \cdot (2 x + 5) = \frac{3}{8}$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $2$ by $2$ .

$\frac{4 + 1}{2} x - \frac{3}{4} \cdot (2 x + 5) = \frac{3}{8}$

Step 1.1.1.2.4.2

Add $4$ and $1$ .

$\frac{5}{2} x - \frac{3}{4} \cdot (2 x + 5) = \frac{3}{8}$

Step 1.1.2

Simplify each term.

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Step 1.1.2.1

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

$\frac{5 x}{2} - \frac{3}{4} \cdot (2 x + 5) = \frac{3}{8}$

Step 1.1.2.2

Apply the distributive property.

$\frac{5 x}{2} - \frac{3}{4} (2 x) - \frac{3}{4} \cdot 5 = \frac{3}{8}$

Step 1.1.2.3

Cancel the common factor of $2$ .

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Step 1.1.2.3.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{5 x}{2} + \frac{- 3}{4} (2 x) - \frac{3}{4} \cdot 5 = \frac{3}{8}$

Step 1.1.2.3.2

Factor $2$ out of $4$ .

$\frac{5 x}{2} + \frac{- 3}{2 (2)} (2 x) - \frac{3}{4} \cdot 5 = \frac{3}{8}$

Step 1.1.2.3.3

Factor $2$ out of $2 x$ .

$\frac{5 x}{2} + \frac{- 3}{2 (2)} (2 (x)) - \frac{3}{4} \cdot 5 = \frac{3}{8}$

Step 1.1.2.3.4

Cancel the common factor.

$\frac{5 x}{2} + \frac{- 3}{2 \cdot 2} (2 x) - \frac{3}{4} \cdot 5 = \frac{3}{8}$

Step 1.1.2.3.5

Rewrite the expression.

$\frac{5 x}{2} + \frac{- 3}{2} x - \frac{3}{4} \cdot 5 = \frac{3}{8}$

Step 1.1.2.4

Combine $\frac{- 3}{2}$ and $x$ .

$\frac{5 x}{2} + \frac{- 3 x}{2} - \frac{3}{4} \cdot 5 = \frac{3}{8}$

Step 1.1.2.5

Multiply $- \frac{3}{4} \cdot 5$ .

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Step 1.1.2.5.1

Multiply $5$ by $- 1$ .

$\frac{5 x}{2} + \frac{- 3 x}{2} - 5 (\frac{3}{4}) = \frac{3}{8}$

Step 1.1.2.5.2

Combine $- 5$ and $\frac{3}{4}$ .

$\frac{5 x}{2} + \frac{- 3 x}{2} + \frac{- 5 \cdot 3}{4} = \frac{3}{8}$

Step 1.1.2.5.3

Multiply $- 5$ by $3$ .

$\frac{5 x}{2} + \frac{- 3 x}{2} + \frac{- 15}{4} = \frac{3}{8}$

Step 1.1.2.6

Simplify each term.

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Step 1.1.2.6.1

Move the negative in front of the fraction.

$\frac{5 x}{2} - \frac{3 x}{2} + \frac{- 15}{4} = \frac{3}{8}$

Step 1.1.2.6.2

Move the negative in front of the fraction.

$\frac{5 x}{2} - \frac{3 x}{2} - \frac{15}{4} = \frac{3}{8}$

Step 1.1.3

Simplify terms.

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Step 1.1.3.1

Combine the numerators over the common denominator.

$\frac{5 x - 3 x}{2} + \frac{- 15}{4} = \frac{3}{8}$

Step 1.1.3.2

Subtract $3 x$ from $5 x$ .

$\frac{2 x}{2} + \frac{- 15}{4} = \frac{3}{8}$

Step 1.1.4

Simplify each term.

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Step 1.1.4.1

Cancel the common factor of $2$ .

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Step 1.1.4.1.1

Cancel the common factor.

$\frac{2 x}{2} + \frac{- 15}{4} = \frac{3}{8}$

Step 1.1.4.1.2

Divide $x$ by $1$ .

$x + \frac{- 15}{4} = \frac{3}{8}$

Step 1.1.4.2

Move the negative in front of the fraction.

$x - \frac{15}{4} = \frac{3}{8}$

Step 2

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

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Step 2.1

Add $\frac{15}{4}$ to both sides of the equation.

$x = \frac{3}{8} + \frac{15}{4}$

Step 2.2

To write $\frac{15}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = \frac{3}{8} + \frac{15}{4} \cdot \frac{2}{2}$

Step 2.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{15}{4}$ by $\frac{2}{2}$ .

$x = \frac{3}{8} + \frac{15 \cdot 2}{4 \cdot 2}$

Step 2.3.2

Multiply $4$ by $2$ .

$x = \frac{3}{8} + \frac{15 \cdot 2}{8}$

Step 2.4

Combine the numerators over the common denominator.

$x = \frac{3 + 15 \cdot 2}{8}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $15$ by $2$ .

$x = \frac{3 + 30}{8}$

Step 2.5.2

Add $3$ and $30$ .

$x = \frac{33}{8}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{33}{8}$

Decimal Form:

$x = 4.125$

Mixed Number Form:

$x = 4 \frac{1}{8}$