Pre-Algebra Examples

$4 y < 20 x$

Step 1

Divide each term in $4 y < 20 x$ by $4$ and simplify.

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Step 1.1

Divide each term in $4 y < 20 x$ by $4$ .

$\frac{4 y}{4} < \frac{20 x}{4}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $4$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{4 y}{4} < \frac{20 x}{4}$

Step 1.2.1.2

Divide $y$ by $1$ .

$y < \frac{20 x}{4}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Cancel the common factor of $20$ and $4$ .

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Step 1.3.1.1

Factor $4$ out of $20 x$ .

$y < \frac{4 (5 x)}{4}$

Step 1.3.1.2

Cancel the common factors.

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Step 1.3.1.2.1

Factor $4$ out of $4$ .

$y < \frac{4 (5 x)}{4 (1)}$

Step 1.3.1.2.2

Cancel the common factor.

$y < \frac{4 (5 x)}{4 \cdot 1}$

Step 1.3.1.2.3

Rewrite the expression.

$y < \frac{5 x}{1}$

Step 1.3.1.2.4

Divide $5 x$ by $1$ .

$y < 5 x$

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 $y = m x + b$ .

$m = 5$

$b = 0$

Step 2.3

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

Slope: $5$

y-intercept: $(0, 0)$

Slope: $5$

y-intercept: $(0, 0)$

Step 3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $5 x$ .

$y < 5 x$

Step 4