Algebra Examples

$5.04 - x = x - 5 \frac{1}{4}$

Step 1

Simplify the right side.

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Step 1.1

Convert $5 \frac{1}{4}$ to an improper fraction.

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Step 1.1.1

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

$5.04 - x = x - (5 + \frac{1}{4})$

Step 1.1.2

Add $5$ and $\frac{1}{4}$ .

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Step 1.1.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$5.04 - x = x - (5 \cdot \frac{4}{4} + \frac{1}{4})$

Step 1.1.2.2

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

$5.04 - x = x - (\frac{5 \cdot 4}{4} + \frac{1}{4})$

Step 1.1.2.3

Combine the numerators over the common denominator.

$5.04 - x = x - \frac{5 \cdot 4 + 1}{4}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $5$ by $4$ .

$5.04 - x = x - \frac{20 + 1}{4}$

Step 1.1.2.4.2

Add $20$ and $1$ .

$5.04 - x = x - \frac{21}{4}$

Step 2

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

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Step 2.1

Subtract $x$ from both sides of the equation.

$5.04 - x - x = - \frac{21}{4}$

Step 2.2

Subtract $x$ from $- x$ .

$5.04 - 2 x = - \frac{21}{4}$

Step 3

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

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Step 3.1

Subtract $5.04$ from both sides of the equation.

$- 2 x = - \frac{21}{4} - 5.04$

Step 3.2

To write $- 5.04$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- 2 x = - \frac{21}{4} - 5.04 \cdot \frac{4}{4}$

Step 3.3

Combine $- 5.04$ and $\frac{4}{4}$ .

$- 2 x = - \frac{21}{4} + \frac{- 5.04 \cdot 4}{4}$

Step 3.4

Combine the numerators over the common denominator.

$- 2 x = \frac{- 21 - 5.04 \cdot 4}{4}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 5.04$ by $4$ .

$- 2 x = \frac{- 21 - 20.16}{4}$

Step 3.5.2

Subtract $20.16$ from $- 21$ .

$- 2 x = \frac{- 41.16}{4}$

Step 3.6

Divide $- 41.16$ by $4$ .

$- 2 x = - 10.29$

Step 4

Divide each term in $- 2 x = - 10.29$ by $- 2$ and simplify.

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Step 4.1

Divide each term in $- 2 x = - 10.29$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 10.29}{- 2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 10.29}{- 2}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 10.29}{- 2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 10.29$ by $- 2$ .

$x = 5.145$