Pre-Algebra Examples

$2 (3 x - 4 y) > 24$

Step 1

Solve for $y$ .

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Step 1.1

Divide each term in $2 (3 x - 4 y) > 24$ by $2$ and simplify.

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Step 1.1.1

Divide each term in $2 (3 x - 4 y) > 24$ by $2$ .

$\frac{2 (3 x - 4 y)}{2} > \frac{24}{2}$

Step 1.1.2

Simplify the left side.

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Step 1.1.2.1

Cancel the common factor of $2$ .

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Step 1.1.2.1.1

Cancel the common factor.

$\frac{2 (3 x - 4 y)}{2} > \frac{24}{2}$

Step 1.1.2.1.2

Divide $3 x - 4 y$ by $1$ .

$3 x - 4 y > \frac{24}{2}$

Step 1.1.3

Simplify the right side.

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Step 1.1.3.1

Divide $24$ by $2$ .

$3 x - 4 y > 12$

Step 1.2

Subtract $3 x$ from both sides of the inequality.

$- 4 y > 12 - 3 x$

Step 1.3

Divide each term in $- 4 y > 12 - 3 x$ by $- 4$ and simplify.

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Step 1.3.1

Divide each term in $- 4 y > 12 - 3 x$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 y}{- 4} < \frac{12}{- 4} + \frac{- 3 x}{- 4}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $- 4$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} < \frac{12}{- 4} + \frac{- 3 x}{- 4}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y < \frac{12}{- 4} + \frac{- 3 x}{- 4}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Divide $12$ by $- 4$ .

$y < - 3 + \frac{- 3 x}{- 4}$

Step 1.3.3.1.2

Dividing two negative values results in a positive value.

$y < - 3 + \frac{3 x}{4}$

Step 2

Find the slope and the y-intercept for the boundary line.

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Step 2.1

Rewrite in slope-intercept form.

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Step 2.1.1

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 2.1.2

Reorder $- 3$ and $\frac{3 x}{4}$ .

$y < \frac{3 x}{4} - 3$

Step 2.1.3

Reorder terms.

$y < \frac{3}{4} x - 3$

Step 2.2

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

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Step 2.2.1

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

$m = \frac{3}{4}$

$b = - 3$

Step 2.2.2

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

Slope: $\frac{3}{4}$

y-intercept: $(0, - 3)$

Slope: $\frac{3}{4}$

y-intercept: $(0, - 3)$

Slope: $\frac{3}{4}$

y-intercept: $(0, - 3)$

Step 3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $- 3 + \frac{3 x}{4}$ .

$y < - 3 + \frac{3 x}{4}$

Step 4