Pre-Algebra Examples

$- 5 y + 7 x = - 5 y + 42$

Step 1

Solve for $y$ .

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Step 1.1

Move all terms containing $y$ to the left side of the equation.

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Step 1.1.1

Add $5 y$ to both sides of the equation.

$- 5 y + 7 x + 5 y = 42$

Step 1.1.2

Combine the opposite terms in $- 5 y + 7 x + 5 y$ .

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Step 1.1.2.1

Add $- 5 y$ and $5 y$ .

$7 x + 0 = 42$

Step 1.1.2.2

Add $7 x$ and $0$ .

$7 x = 42$

Step 1.2

Divide each term in $7 x = 42$ by $7$ and simplify.

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Step 1.2.1

Divide each term in $7 x = 42$ by $7$ .

$\frac{7 x}{7} = \frac{42}{7}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $7$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{42}{7}$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{42}{7}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Divide $42$ by $7$ .

$x = 6$

Step 1.3

The variable $y$ got canceled.

All real numbers

Step 2

Since $x = 6$ 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.

$\begin{array}{c} x & y \\ 6 & 0 \\ 6 & 1 \end{array}$

Step 4

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

Slope: Undefined

y-intercept: No y-intercept

$\begin{array}{c} x & y \\ 6 & 0 \\ 6 & 1 \end{array}$

Step 5