Pre-Algebra Examples

$2 (x - y) < - 5$

Step 1

Solve for $y$ .

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Step 1.1

Divide each term in $2 (x - y) < - 5$ by $2$ and simplify.

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Step 1.1.1

Divide each term in $2 (x - y) < - 5$ by $2$ .

$\frac{2 (x - y)}{2} < \frac{- 5}{2}$

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.

$\frac{2 (x - y)}{2} < \frac{- 5}{2}$

Step 1.1.2.1.2

Divide $x - y$ by $1$ .

$x - y < \frac{- 5}{2}$

Step 1.1.3

Simplify the right side.

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Step 1.1.3.1

Move the negative in front of the fraction.

$x - y < - \frac{5}{2}$

Step 1.2

Subtract $x$ from both sides of the inequality.

$- y < - \frac{5}{2} - x$

Step 1.3

Divide each term in $- y < - \frac{5}{2} - x$ by $- 1$ and simplify.

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Step 1.3.1

Divide each term in $- y < - \frac{5}{2} - x$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} > \frac{- \frac{5}{2}}{- 1} + \frac{- x}{- 1}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} > \frac{- \frac{5}{2}}{- 1} + \frac{- x}{- 1}$

Step 1.3.2.2

Divide $y$ by $1$ .

$y > \frac{- \frac{5}{2}}{- 1} + \frac{- x}{- 1}$

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

Dividing two negative values results in a positive value.

$y > \frac{\frac{5}{2}}{1} + \frac{- x}{- 1}$

Step 1.3.3.1.2

Divide $\frac{5}{2}$ by $1$ .

$y > \frac{5}{2} + \frac{- x}{- 1}$

Step 1.3.3.1.3

Dividing two negative values results in a positive value.

$y > \frac{5}{2} + \frac{x}{1}$

Step 1.3.3.1.4

Divide $x$ by $1$ .

$y > \frac{5}{2} + x$

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 $\frac{5}{2}$ and $x$ .

$y > x + \frac{5}{2}$

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 $y = m x + b$ .

$m = 1$

$b = \frac{5}{2}$

Step 2.2.2

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

Slope: $1$

y-intercept: $(0, \frac{5}{2})$

Slope: $1$

y-intercept: $(0, \frac{5}{2})$

Slope: $1$

y-intercept: $(0, \frac{5}{2})$

Step 3

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $\frac{5}{2} + x$ .

$y > \frac{5}{2} + x$

Step 4