Pre-Algebra Examples

$x + 7 = \frac{1}{2} \cdot (y - 5)$

Step 1

Solve for $y$ .

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Step 1.1

Rewrite the equation as $\frac{y}{2} - \frac{5}{2} = x + 7$ .

$\frac{y}{2} - \frac{5}{2} = x + 7$

Step 1.2

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

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Step 1.2.1

Add $\frac{5}{2}$ to both sides of the equation.

$\frac{y}{2} = x + 7 + \frac{5}{2}$

Step 1.2.2

To write $7$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{y}{2} = x + 7 \cdot \frac{2}{2} + \frac{5}{2}$

Step 1.2.3

Combine $7$ and $\frac{2}{2}$ .

$\frac{y}{2} = x + \frac{7 \cdot 2}{2} + \frac{5}{2}$

Step 1.2.4

Combine the numerators over the common denominator.

$\frac{y}{2} = x + \frac{7 \cdot 2 + 5}{2}$

Step 1.2.5

Simplify the numerator.

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Step 1.2.5.1

Multiply $7$ by $2$ .

$\frac{y}{2} = x + \frac{14 + 5}{2}$

Step 1.2.5.2

Add $14$ and $5$ .

$\frac{y}{2} = x + \frac{19}{2}$

Step 1.3

Multiply both sides of the equation by $2$ .

$2 \frac{y}{2} = 2 (x + \frac{19}{2})$

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 $2$ .

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Step 1.4.1.1.1

Cancel the common factor.

$2 \frac{y}{2} = 2 (x + \frac{19}{2})$

Step 1.4.1.1.2

Rewrite the expression.

$y = 2 (x + \frac{19}{2})$

Step 1.4.2

Simplify the right side.

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Step 1.4.2.1

Simplify $2 (x + \frac{19}{2})$ .

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Step 1.4.2.1.1

Apply the distributive property.

$y = 2 x + 2 (\frac{19}{2})$

Step 1.4.2.1.2

Cancel the common factor of $2$ .

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Step 1.4.2.1.2.1

Cancel the common factor.

$y = 2 x + 2 (\frac{19}{2})$

Step 1.4.2.1.2.2

Rewrite the expression.

$y = 2 x + 19$

Step 2

Use the slope-intercept form to find the slope and y-intercept.

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Step 2.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 2.2

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = 2$

$b = 19$

Step 2.3

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $2$

y-intercept: $(0, 19)$

Slope: $2$

y-intercept: $(0, 19)$

Step 3

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

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Step 3.1

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ 0 & 19 \\ 1 & 21 \end{array}$

Step 4

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

Slope: $2$

y-intercept: $(0, 19)$

$\begin{array}{c} x & y \\ 0 & 19 \\ 1 & 21 \end{array}$

Step 5