Pre-Algebra Examples

$7 x + 13 < - 7 y + 13$

Step 1

Solve for $y$ .

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Step 1.1

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

$- 7 y + 13 > 7 x + 13$

Step 1.2

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

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Step 1.2.1

Subtract $13$ from both sides of the inequality.

$- 7 y > 7 x + 13 - 13$

Step 1.2.2

Combine the opposite terms in $7 x + 13 - 13$ .

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Step 1.2.2.1

Subtract $13$ from $13$ .

$- 7 y > 7 x + 0$

Step 1.2.2.2

Add $7 x$ and $0$ .

$- 7 y > 7 x$

Step 1.3

Divide each term in $- 7 y > 7 x$ by $- 7$ and simplify.

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Step 1.3.1

Divide each term in $- 7 y > 7 x$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 y}{- 7} < \frac{7 x}{- 7}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $- 7$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{- 7 y}{- 7} < \frac{7 x}{- 7}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y < \frac{7 x}{- 7}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Cancel the common factor of $7$ and $- 7$ .

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Step 1.3.3.1.1

Factor $7$ out of $7 x$ .

$y < \frac{7 (x)}{- 7}$

Step 1.3.3.1.2

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

$y < - 1 \cdot x$

Step 1.3.3.2

Rewrite $- 1 \cdot x$ as $- x$ .

$y < - x$

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 $y = m x + b$ .

$m = - 1$

$b = 0$

Step 2.3

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

Slope: $- 1$

y-intercept: $(0, 0)$

Slope: $- 1$

y-intercept: $(0, 0)$

Step 3

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

$y < - x$

Step 4