Basic Math Examples

$\frac{5}{2} x - (\frac{2}{5} - \frac{1}{4} x) = \frac{5}{4} x + \frac{1}{10}$

Step 1

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

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$\frac{5 x}{2} - (\frac{2}{5} - \frac{1}{4} x) = \frac{5}{4} x + \frac{1}{10}$

Step 1.1.2

Combine $x$ and $\frac{1}{4}$ .

$\frac{5 x}{2} - (\frac{2}{5} - \frac{x}{4}) = \frac{5}{4} x + \frac{1}{10}$

Step 1.1.3

Apply the distributive property.

$\frac{5 x}{2} - \frac{2}{5} - - \frac{x}{4} = \frac{5}{4} x + \frac{1}{10}$

Step 1.1.4

Multiply $- - \frac{x}{4}$ .

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Step 1.1.4.1

Multiply $- 1$ by $- 1$ .

$\frac{5 x}{2} - \frac{2}{5} + 1 \frac{x}{4} = \frac{5}{4} x + \frac{1}{10}$

Step 1.1.4.2

Multiply $\frac{x}{4}$ by $1$ .

$\frac{5 x}{2} - \frac{2}{5} + \frac{x}{4} = \frac{5}{4} x + \frac{1}{10}$

Step 1.2

To write $\frac{5 x}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 x}{2} \cdot \frac{2}{2} + \frac{x}{4} - \frac{2}{5} = \frac{5}{4} x + \frac{1}{10}$

Step 1.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{5 x}{2}$ by $\frac{2}{2}$ .

$\frac{5 x \cdot 2}{2 \cdot 2} + \frac{x}{4} - \frac{2}{5} = \frac{5}{4} x + \frac{1}{10}$

Step 1.3.2

Multiply $2$ by $2$ .

$\frac{5 x \cdot 2}{4} + \frac{x}{4} - \frac{2}{5} = \frac{5}{4} x + \frac{1}{10}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{5 x \cdot 2 + x}{4} - \frac{2}{5} = \frac{5}{4} x + \frac{1}{10}$

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 $x$ out of $5 x \cdot 2 + x$ .

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Step 1.5.1.1.1

Factor $x$ out of $5 x \cdot 2$ .

$\frac{x (5 \cdot 2) + x}{4} - \frac{2}{5} = \frac{5}{4} x + \frac{1}{10}$

Step 1.5.1.1.2

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

$\frac{x (5 \cdot 2) + x^{1}}{4} - \frac{2}{5} = \frac{5}{4} x + \frac{1}{10}$

Step 1.5.1.1.3

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

$\frac{x (5 \cdot 2) + x \cdot 1}{4} - \frac{2}{5} = \frac{5}{4} x + \frac{1}{10}$

Step 1.5.1.1.4

Factor $x$ out of $x (5 \cdot 2) + x \cdot 1$ .

$\frac{x (5 \cdot 2 + 1)}{4} - \frac{2}{5} = \frac{5}{4} x + \frac{1}{10}$

Step 1.5.1.2

Multiply $5$ by $2$ .

$\frac{x (10 + 1)}{4} - \frac{2}{5} = \frac{5}{4} x + \frac{1}{10}$

Step 1.5.1.3

Add $10$ and $1$ .

$\frac{x \cdot 11}{4} - \frac{2}{5} = \frac{5}{4} x + \frac{1}{10}$

Step 1.5.2

Move $11$ to the left of $x$ .

$\frac{11 x}{4} - \frac{2}{5} = \frac{5}{4} x + \frac{1}{10}$

Step 2

Combine $\frac{5}{4}$ and $x$ .

$\frac{11 x}{4} - \frac{2}{5} = \frac{5 x}{4} + \frac{1}{10}$

Step 3

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

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Step 3.1

Subtract $\frac{5 x}{4}$ from both sides of the equation.

$\frac{11 x}{4} - \frac{2}{5} - \frac{5 x}{4} = \frac{1}{10}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{11 x - 5 x}{4} + \frac{- 2}{5} = \frac{1}{10}$

Step 3.3

Subtract $5 x$ from $11 x$ .

$\frac{6 x}{4} + \frac{- 2}{5} = \frac{1}{10}$

Step 3.4

Simplify each term.

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Step 3.4.1

Cancel the common factor of $6$ and $4$ .

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Step 3.4.1.1

Factor $2$ out of $6 x$ .

$\frac{2 (3 x)}{4} + \frac{- 2}{5} = \frac{1}{10}$

Step 3.4.1.2

Cancel the common factors.

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Step 3.4.1.2.1

Factor $2$ out of $4$ .

$\frac{2 (3 x)}{2 (2)} + \frac{- 2}{5} = \frac{1}{10}$

Step 3.4.1.2.2

Cancel the common factor.

$\frac{2 (3 x)}{2 \cdot 2} + \frac{- 2}{5} = \frac{1}{10}$

Step 3.4.1.2.3

Rewrite the expression.

$\frac{3 x}{2} + \frac{- 2}{5} = \frac{1}{10}$

Step 3.4.2

Move the negative in front of the fraction.

$\frac{3 x}{2} - \frac{2}{5} = \frac{1}{10}$

Step 4

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

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Step 4.1

Add $\frac{2}{5}$ to both sides of the equation.

$\frac{3 x}{2} = \frac{1}{10} + \frac{2}{5}$

Step 4.2

To write $\frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 x}{2} = \frac{1}{10} + \frac{2}{5} \cdot \frac{2}{2}$

Step 4.3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.3.1

Multiply $\frac{2}{5}$ by $\frac{2}{2}$ .

$\frac{3 x}{2} = \frac{1}{10} + \frac{2 \cdot 2}{5 \cdot 2}$

Step 4.3.2

Multiply $5$ by $2$ .

$\frac{3 x}{2} = \frac{1}{10} + \frac{2 \cdot 2}{10}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{3 x}{2} = \frac{1 + 2 \cdot 2}{10}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $2$ by $2$ .

$\frac{3 x}{2} = \frac{1 + 4}{10}$

Step 4.5.2

Add $1$ and $4$ .

$\frac{3 x}{2} = \frac{5}{10}$

Step 4.6

Cancel the common factor of $5$ and $10$ .

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Step 4.6.1

Factor $5$ out of $5$ .

$\frac{3 x}{2} = \frac{5 (1)}{10}$

Step 4.6.2

Cancel the common factors.

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Step 4.6.2.1

Factor $5$ out of $10$ .

$\frac{3 x}{2} = \frac{5 \cdot 1}{5 \cdot 2}$

Step 4.6.2.2

Cancel the common factor.

$\frac{3 x}{2} = \frac{5 \cdot 1}{5 \cdot 2}$

Step 4.6.2.3

Rewrite the expression.

$\frac{3 x}{2} = \frac{1}{2}$

Step 5

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$3 x = 1$

Step 6

Divide each term in $3 x = 1$ by $3$ and simplify.

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Step 6.1

Divide each term in $3 x = 1$ by $3$ .

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

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $3$ .

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Step 6.2.1.1

Cancel the common factor.

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

Step 6.2.1.2

Divide $x$ by $1$ .

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.\overline{3}$