Pre-Algebra Examples

$6 - y > 7 - 2 x$

Step 1

Solve for $y$ .

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Step 1.1

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

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Step 1.1.1

Subtract $6$ from both sides of the inequality.

$- y > 7 - 2 x - 6$

Step 1.1.2

Subtract $6$ from $7$ .

$- y > - 2 x + 1$

Step 1.2

Divide each term in $- y > - 2 x + 1$ by $- 1$ and simplify.

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Step 1.2.1

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

$\frac{- y}{- 1} < \frac{- 2 x}{- 1} + \frac{1}{- 1}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} < \frac{- 2 x}{- 1} + \frac{1}{- 1}$

Step 1.2.2.2

Divide $y$ by $1$ .

$y < \frac{- 2 x}{- 1} + \frac{1}{- 1}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

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

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

Step 1.2.3.1.2

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

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

Step 1.2.3.1.3

Multiply $- 2$ by $- 1$ .

$y < 2 x + \frac{1}{- 1}$

Step 1.2.3.1.4

Divide $1$ by $- 1$ .

$y < 2 x - 1$

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 $y = m x + b$ .

$m = 2$

$b = - 1$

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: $(0, - 1)$

Slope: $2$

y-intercept: $(0, - 1)$

Step 3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $2 x - 1$ .

$y < 2 x - 1$

Step 4