Algebra Examples

$3 (x - 2) > y + 8$

Step 1

Solve for $y$ .

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Step 1.1

Rewrite so $y$ is on the left side of the inequality.

$y + 8 < 3 (x - 2)$

Step 1.2

Simplify $3 (x - 2)$ .

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Step 1.2.1

Rewrite.

$y + 8 < 0 + 0 + 3 (x - 2)$

Step 1.2.2

Simplify by adding zeros.

$y + 8 < 3 (x - 2)$

Step 1.2.3

Apply the distributive property.

$y + 8 < 3 x + 3 \cdot - 2$

Step 1.2.4

Multiply $3$ by $- 2$ .

$y + 8 < 3 x - 6$

Step 1.3

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

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Step 1.3.1

Subtract $8$ from both sides of the inequality.

$y < 3 x - 6 - 8$

Step 1.3.2

Subtract $8$ from $- 6$ .

$y < 3 x - 14$

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 $y = m x + b$ .

$m = 3$

$b = - 14$

Step 2.3

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

Slope: $3$

y-intercept: $(0, - 14)$

Slope: $3$

y-intercept: $(0, - 14)$

Step 3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $3 x - 14$ .

$y < 3 x - 14$

Step 4