Pre-Algebra Examples

$\frac{7}{8} = \frac{1}{4} X + \frac{1}{2}$

Step 1

Solve for $y$ .

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Step 1.1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$\frac{x}{4} + \frac{1}{2} = \frac{7}{8}$

Step 1.2

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

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Step 1.2.1

Subtract $\frac{1}{2}$ from both sides of the equation.

$\frac{x}{4} = \frac{7}{8} - \frac{1}{2}$

Step 1.2.2

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x}{4} = \frac{7}{8} - \frac{1}{2} \cdot \frac{4}{4}$

Step 1.2.3

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

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Step 1.2.3.1

Multiply $\frac{1}{2}$ by $\frac{4}{4}$ .

$\frac{x}{4} = \frac{7}{8} - \frac{4}{2 \cdot 4}$

Step 1.2.3.2

Multiply $2$ by $4$ .

$\frac{x}{4} = \frac{7}{8} - \frac{4}{8}$

Step 1.2.4

Combine the numerators over the common denominator.

$\frac{x}{4} = \frac{7 - 4}{8}$

Step 1.2.5

Subtract $4$ from $7$ .

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

Step 1.3

Multiply both sides of the equation by $4$ .

$4 \frac{x}{4} = 4 (\frac{3}{8})$

Step 1.4

Simplify both sides of the equation.

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Step 1.4.1

Simplify the left side.

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Step 1.4.1.1

Cancel the common factor of $4$ .

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Step 1.4.1.1.1

Cancel the common factor.

$4 \frac{x}{4} = 4 (\frac{3}{8})$

Step 1.4.1.1.2

Rewrite the expression.

$x = 4 (\frac{3}{8})$

Step 1.4.2

Simplify the right side.

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Step 1.4.2.1

Cancel the common factor of $4$ .

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Step 1.4.2.1.1

Factor $4$ out of $8$ .

$x = 4 \frac{3}{4 (2)}$

Step 1.4.2.1.2

Cancel the common factor.

$x = 4 \frac{3}{4 \cdot 2}$

Step 1.4.2.1.3

Rewrite the expression.

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

Step 2

Since $x = \frac{3}{2}$ is a vertical line, there is no y-intercept and the slope is undefined.

Slope: Undefined

y-intercept: No y-intercept

Step 3

Find two points on the line.

$\begin{array}{c} x & y \\ \frac{3}{2} & 0 \\ \frac{3}{2} & 1 \end{array}$

Step 4

Graph the line using the slope, y-intercept, and two points.

Slope: Undefined

y-intercept: No y-intercept

$\begin{array}{c} x & y \\ \frac{3}{2} & 0 \\ \frac{3}{2} & 1 \end{array}$

Step 5