Pre-Algebra Examples

$\frac{3}{4} = \frac{x - 1}{2}$

Step 1

Solve for $y$ .

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Step 1.1

Multiply both sides by $2$ .

$\frac{3}{4} \cdot 2 = \frac{x - 1}{2} \cdot 2$

Step 1.2

Simplify.

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Step 1.2.1

Simplify the left side.

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Step 1.2.1.1

Cancel the common factor of $2$ .

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Step 1.2.1.1.1

Factor $2$ out of $4$ .

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

Step 1.2.1.1.2

Cancel the common factor.

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

Step 1.2.1.1.3

Rewrite the expression.

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

Step 1.2.2

Simplify the right side.

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Step 1.2.2.1

Cancel the common factor of $2$ .

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Step 1.2.2.1.1

Cancel the common factor.

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

Step 1.2.2.1.2

Rewrite the expression.

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

Step 1.3

Solve for $x$ .

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Step 1.3.1

Rewrite the equation as $x - 1 = \frac{3}{2}$ .

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

Step 1.3.2

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

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Step 1.3.2.1

Add $1$ to both sides of the equation.

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

Step 1.3.2.2

Write $1$ as a fraction with a common denominator.

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

Step 1.3.2.3

Combine the numerators over the common denominator.

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

Step 1.3.2.4

Add $3$ and $2$ .

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

Step 2

Since $x = \frac{5}{2}$ 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.

$\begin{array}{c} x & y \\ \frac{5}{2} & 0 \\ \frac{5}{2} & 1 \end{array}$

Step 4

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

Slope: Undefined

y-intercept: No y-intercept

$\begin{array}{c} x & y \\ \frac{5}{2} & 0 \\ \frac{5}{2} & 1 \end{array}$

Step 5