Pre-Algebra Examples

$- x < 0.1 y$

Step 1

Solve for $y$ .

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Step 1.1

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

$0.1 y > - x$

Step 1.2

Divide each term in $0.1 y > - x$ by $0.1$ and simplify.

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Step 1.2.1

Divide each term in $0.1 y > - x$ by $0.1$ .

$\frac{0.1 y}{0.1} > \frac{- x}{0.1}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $0.1$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{0.1 y}{0.1} > \frac{- x}{0.1}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y > \frac{- x}{0.1}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Move the negative in front of the fraction.

$y > - \frac{x}{0.1}$

Step 1.2.3.2

Multiply by $1$ .

$y > - \frac{1 x}{0.1}$

Step 1.2.3.3

Factor $0.1$ out of $0.1$ .

$y > - \frac{1 x}{0.1 (1)}$

Step 1.2.3.4

Separate fractions.

$y > - (\frac{1}{0.1} \cdot \frac{x}{1})$

Step 1.2.3.5

Divide $1$ by $0.1$ .

$y > - (10 \frac{x}{1})$

Step 1.2.3.6

Divide $x$ by $1$ .

$y > - (10 x)$

Step 1.2.3.7

Multiply $10$ by $- 1$ .

$y > - 10 x$

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 $y = m x + b$ .

$m = - 10$

$b = 0$

Step 2.3

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

Slope: $- 10$

y-intercept: $(0, 0)$

Slope: $- 10$

y-intercept: $(0, 0)$

Step 3

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $- 10 x$ .

$y > - 10 x$

Step 4