Pre-Algebra Examples

$\frac{5}{8} x + \frac{1}{16} x = \frac{11}{16} + x$

Step 1

Simplify $\frac{5}{8} x + \frac{1}{16} x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{5}{8}$ and $x$ .

$\frac{5 x}{8} + \frac{1}{16} x = \frac{11}{16} + x$

Step 1.1.2

Combine $\frac{1}{16}$ and $x$ .

$\frac{5 x}{8} + \frac{x}{16} = \frac{11}{16} + x$

Step 1.2

To write $\frac{5 x}{8}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 x}{8} \cdot \frac{2}{2} + \frac{x}{16} = \frac{11}{16} + x$

Step 1.3

Write each expression with a common denominator of $16$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{5 x}{8}$ by $\frac{2}{2}$ .

$\frac{5 x \cdot 2}{8 \cdot 2} + \frac{x}{16} = \frac{11}{16} + x$

Step 1.3.2

Multiply $8$ by $2$ .

$\frac{5 x \cdot 2}{16} + \frac{x}{16} = \frac{11}{16} + x$

Step 1.4

Combine the numerators over the common denominator.

$\frac{5 x \cdot 2 + x}{16} = \frac{11}{16} + x$

Step 1.5

Simplify the numerator.

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Step 1.5.1

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

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Step 1.5.1.1

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

$\frac{x (5 \cdot 2) + x}{16} = \frac{11}{16} + x$

Step 1.5.1.2

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

$\frac{x (5 \cdot 2) + x^{1}}{16} = \frac{11}{16} + x$

Step 1.5.1.3

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

$\frac{x (5 \cdot 2) + x \cdot 1}{16} = \frac{11}{16} + x$

Step 1.5.1.4

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

$\frac{x (5 \cdot 2 + 1)}{16} = \frac{11}{16} + x$

Step 1.5.2

Multiply $5$ by $2$ .

$\frac{x (10 + 1)}{16} = \frac{11}{16} + x$

Step 1.5.3

Add $10$ and $1$ .

$\frac{x \cdot 11}{16} = \frac{11}{16} + x$

Step 1.6

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

$\frac{11 x}{16} = \frac{11}{16} + x$

Step 2

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

$x = - \frac{11}{5}$

Step 3