Pre-Algebra Examples

$2 x > 6 - y$

Step 1

Solve for $y$ .

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Step 1.1

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

$6 - y < 2 x$

Step 1.2

Subtract $6$ from both sides of the inequality.

$- y < 2 x - 6$

Step 1.3

Divide each term in $- y < 2 x - 6$ by $- 1$ and simplify.

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Step 1.3.1

Divide each term in $- y < 2 x - 6$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} > \frac{2 x}{- 1} + \frac{- 6}{- 1}$

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.

$\frac{y}{1} > \frac{2 x}{- 1} + \frac{- 6}{- 1}$

Step 1.3.2.2

Divide $y$ by $1$ .

$y > \frac{2 x}{- 1} + \frac{- 6}{- 1}$

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

Move the negative one from the denominator of $\frac{2 x}{- 1}$ .

$y > - 1 \cdot (2 x) + \frac{- 6}{- 1}$

Step 1.3.3.1.2

Rewrite $- 1 \cdot (2 x)$ as $- (2 x)$ .

$y > - (2 x) + \frac{- 6}{- 1}$

Step 1.3.3.1.3

Multiply $2$ by $- 1$ .

$y > - 2 x + \frac{- 6}{- 1}$

Step 1.3.3.1.4

Divide $- 6$ by $- 1$ .

$y > - 2 x + 6$

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 above the boundary line since $y$ is greater than $- 2 x + 6$ .

$y > - 2 x + 6$

Step 4