Pre-Algebra Examples

$- 2 x + 2 y - 4 < 0$

Step 1

Solve for $y$ .

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Step 1.1

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

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Step 1.1.1

Add $2 x$ to both sides of the inequality.

$2 y - 4 < 2 x$

Step 1.1.2

Add $4$ to both sides of the inequality.

$2 y < 2 x + 4$

Step 1.2

Divide each term in $2 y < 2 x + 4$ by $2$ and simplify.

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Step 1.2.1

Divide each term in $2 y < 2 x + 4$ by $2$ .

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

Step 1.2.2

Simplify the left 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.

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

Step 1.2.2.1.2

Divide $y$ by $1$ .

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

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Cancel the common factor of $2$ .

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Step 1.2.3.1.1.1

Cancel the common factor.

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

Step 1.2.3.1.1.2

Divide $x$ by $1$ .

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

Step 1.2.3.1.2

Divide $4$ by $2$ .

$y < x + 2$

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 $y = m x + b$ .

$m = 1$

$b = 2$

Step 2.3

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

Slope: $1$

y-intercept: $(0, 2)$

Slope: $1$

y-intercept: $(0, 2)$

Step 3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $x + 2$ .

$y < x + 2$

Step 4