Pre-Algebra Examples

$6 - 2 y > 18 - 4 x$

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

Subtract $6$ from both sides of the inequality.

$- 2 y > 18 - 4 x - 6$

Step 1.1.2

Subtract $6$ from $18$ .

$- 2 y > - 4 x + 12$

Step 1.2

Divide each term in $- 2 y > - 4 x + 12$ by $- 2$ and simplify.

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Step 1.2.1

Divide each term in $- 2 y > - 4 x + 12$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 y}{- 2} < \frac{- 4 x}{- 2} + \frac{12}{- 2}$

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.

$\frac{- 2 y}{- 2} < \frac{- 4 x}{- 2} + \frac{12}{- 2}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y < \frac{- 4 x}{- 2} + \frac{12}{- 2}$

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 $- 4$ and $- 2$ .

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Step 1.2.3.1.1.1

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

$y < \frac{- 2 (2 x)}{- 2} + \frac{12}{- 2}$

Step 1.2.3.1.1.2

Cancel the common factors.

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Step 1.2.3.1.1.2.1

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

$y < \frac{- 2 (2 x)}{- 2 (1)} + \frac{12}{- 2}$

Step 1.2.3.1.1.2.2

Cancel the common factor.

$y < \frac{- 2 (2 x)}{- 2 \cdot 1} + \frac{12}{- 2}$

Step 1.2.3.1.1.2.3

Rewrite the expression.

$y < \frac{2 x}{1} + \frac{12}{- 2}$

Step 1.2.3.1.1.2.4

Divide $2 x$ by $1$ .

$y < 2 x + \frac{12}{- 2}$

Step 1.2.3.1.2

Divide $12$ by $- 2$ .

$y < 2 x - 6$

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 $y = m x + b$ .

$m = 2$

$b = - 6$

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: $(0, - 6)$

Slope: $2$

y-intercept: $(0, - 6)$

Step 3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $2 x - 6$ .

$y < 2 x - 6$

Step 4