Pre-Algebra Examples

$2 x - 4 y > 4$

Step 1

Write in $y = m x + b$ form.

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Step 1.1

Solve for $y$ .

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Step 1.1.1

Subtract $2 x$ from both sides of the inequality.

$- 4 y > 4 - 2 x$

Step 1.1.2

Divide each term in $- 4 y > 4 - 2 x$ by $- 4$ and simplify.

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Step 1.1.2.1

Divide each term in $- 4 y > 4 - 2 x$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 y}{- 4} < \frac{4}{- 4} + \frac{- 2 x}{- 4}$

Step 1.1.2.2

Simplify the left side.

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Step 1.1.2.2.1

Cancel the common factor of $- 4$ .

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Step 1.1.2.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} < \frac{4}{- 4} + \frac{- 2 x}{- 4}$

Step 1.1.2.2.1.2

Divide $y$ by $1$ .

$y < \frac{4}{- 4} + \frac{- 2 x}{- 4}$

Step 1.1.2.3

Simplify the right side.

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Step 1.1.2.3.1

Simplify each term.

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Step 1.1.2.3.1.1

Divide $4$ by $- 4$ .

$y < - 1 + \frac{- 2 x}{- 4}$

Step 1.1.2.3.1.2

Cancel the common factor of $- 2$ and $- 4$ .

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Step 1.1.2.3.1.2.1

Factor $- 2$ out of $- 2 x$ .

$y < - 1 + \frac{- 2 (x)}{- 4}$

Step 1.1.2.3.1.2.2

Cancel the common factors.

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Step 1.1.2.3.1.2.2.1

Factor $- 2$ out of $- 4$ .

$y < - 1 + \frac{- 2 (x)}{- 2 (2)}$

Step 1.1.2.3.1.2.2.2

Cancel the common factor.

$y < - 1 + \frac{- 2 x}{- 2 \cdot 2}$

Step 1.1.2.3.1.2.2.3

Rewrite the expression.

$y < - 1 + \frac{x}{2}$

Step 1.2

Rearrange terms.

$y < \frac{x}{2} - 1$

Step 1.3

Reorder terms.

$y < \frac{1}{2} x - 1$

Step 2

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

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Step 2.1

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

$m = \frac{1}{2}$

$b = - 1$

Step 2.2

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

Slope: $\frac{1}{2}$

y-intercept: $(0, - 1)$

Slope: $\frac{1}{2}$

y-intercept: $(0, - 1)$

Step 3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $\frac{1}{2} x - 1$ .

$y < \frac{1}{2} x - 1$

Step 4