Pre-Algebra Examples

$y - 5 > 2 (x - 5)$

Step 1

Solve for $y$ .

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Step 1.1

Simplify $2 (x - 5)$ .

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Step 1.1.1

Rewrite.

$y - 5 > 0 + 0 + 2 (x - 5)$

Step 1.1.2

Simplify by adding zeros.

$y - 5 > 2 (x - 5)$

Step 1.1.3

Apply the distributive property.

$y - 5 > 2 x + 2 \cdot - 5$

Step 1.1.4

Multiply $2$ by $- 5$ .

$y - 5 > 2 x - 10$

Step 1.2

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

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Step 1.2.1

Add $5$ to both sides of the inequality.

$y > 2 x - 10 + 5$

Step 1.2.2

Add $- 10$ and $5$ .

$y > 2 x - 5$

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 $y = m x + b$ .

$m = 2$

$b = - 5$

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: $(0, - 5)$

Slope: $2$

y-intercept: $(0, - 5)$

Step 3

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $2 x - 5$ .

$y > 2 x - 5$

Step 4