Pre-Algebra Examples

$\frac{1}{20} x - \frac{1}{40} + \frac{1}{5} x = \frac{1}{5} + x$

Step 1

Simplify $\frac{1}{20} x - \frac{1}{40} + \frac{1}{5} x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{1}{20}$ and $x$ .

$\frac{x}{20} - \frac{1}{40} + \frac{1}{5} x = \frac{1}{5} + x$

Step 1.1.2

Combine $\frac{1}{5}$ and $x$ .

$\frac{x}{20} - \frac{1}{40} + \frac{x}{5} = \frac{1}{5} + x$

Step 1.2

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

$\frac{x}{20} + \frac{x}{5} \cdot \frac{4}{4} - \frac{1}{40} = \frac{1}{5} + x$

Step 1.3

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{x}{5}$ by $\frac{4}{4}$ .

$\frac{x}{20} + \frac{x \cdot 4}{5 \cdot 4} - \frac{1}{40} = \frac{1}{5} + x$

Step 1.3.2

Multiply $5$ by $4$ .

$\frac{x}{20} + \frac{x \cdot 4}{20} - \frac{1}{40} = \frac{1}{5} + x$

Step 1.4

Combine the numerators over the common denominator.

$\frac{x + x \cdot 4}{20} - \frac{1}{40} = \frac{1}{5} + x$

Step 1.5

Add $x$ and $x \cdot 4$ .

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Step 1.5.1

Reorder $x$ and $4$ .

$\frac{x + 4 \cdot x}{20} - \frac{1}{40} = \frac{1}{5} + x$

Step 1.5.2

Add $x$ and $4 \cdot x$ .

$\frac{5 x}{20} - \frac{1}{40} = \frac{1}{5} + x$

Step 1.6

Cancel the common factor of $5$ and $20$ .

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Step 1.6.1

Factor $5$ out of $5 x$ .

$\frac{5 (x)}{20} - \frac{1}{40} = \frac{1}{5} + x$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $5$ out of $20$ .

$\frac{5 x}{5 \cdot 4} - \frac{1}{40} = \frac{1}{5} + x$

Step 1.6.2.2

Cancel the common factor.

$\frac{5 x}{5 \cdot 4} - \frac{1}{40} = \frac{1}{5} + x$

Step 1.6.2.3

Rewrite the expression.

$\frac{x}{4} - \frac{1}{40} = \frac{1}{5} + x$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx - 0.3$

Step 3