Pre-Algebra Examples

$\frac{2}{5} x + \frac{1}{2} y > \frac{7}{10}$

Step 1

Write in $y = m x + b$ form.

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Step 1.1

Solve for $y$ .

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Combine $\frac{2}{5}$ and $x$ .

$\frac{2 x}{5} + \frac{1}{2} y > \frac{7}{10}$

Step 1.1.1.2

Combine $\frac{1}{2}$ and $y$ .

$\frac{2 x}{5} + \frac{y}{2} > \frac{7}{10}$

Step 1.1.2

Subtract $\frac{2 x}{5}$ from both sides of the inequality.

$\frac{y}{2} > \frac{7}{10} - \frac{2 x}{5}$

Step 1.1.3

Multiply both sides by $2$ .

$\frac{y}{2} \cdot 2 > (\frac{7}{10} - \frac{2 x}{5}) \cdot 2$

Step 1.1.4

Simplify.

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Step 1.1.4.1

Simplify the left side.

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Step 1.1.4.1.1

Cancel the common factor of $2$ .

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Step 1.1.4.1.1.1

Cancel the common factor.

$\frac{y}{2} \cdot 2 > (\frac{7}{10} - \frac{2 x}{5}) \cdot 2$

Step 1.1.4.1.1.2

Rewrite the expression.

$y > (\frac{7}{10} - \frac{2 x}{5}) \cdot 2$

Step 1.1.4.2

Simplify the right side.

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Step 1.1.4.2.1

Simplify $(\frac{7}{10} - \frac{2 x}{5}) \cdot 2$ .

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Step 1.1.4.2.1.1

Apply the distributive property.

$y > \frac{7}{10} \cdot 2 - \frac{2 x}{5} \cdot 2$

Step 1.1.4.2.1.2

Cancel the common factor of $2$ .

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Step 1.1.4.2.1.2.1

Factor $2$ out of $10$ .

$y > \frac{7}{2 (5)} \cdot 2 - \frac{2 x}{5} \cdot 2$

Step 1.1.4.2.1.2.2

Cancel the common factor.

$y > \frac{7}{2 \cdot 5} \cdot 2 - \frac{2 x}{5} \cdot 2$

Step 1.1.4.2.1.2.3

Rewrite the expression.

$y > \frac{7}{5} - \frac{2 x}{5} \cdot 2$

Step 1.1.4.2.1.3

Multiply $- \frac{2 x}{5} \cdot 2$ .

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Step 1.1.4.2.1.3.1

Multiply $2$ by $- 1$ .

$y > \frac{7}{5} - 2 \frac{2 x}{5}$

Step 1.1.4.2.1.3.2

Combine $- 2$ and $\frac{2 x}{5}$ .

$y > \frac{7}{5} + \frac{- 2 (2 x)}{5}$

Step 1.1.4.2.1.3.3

Multiply $2$ by $- 2$ .

$y > \frac{7}{5} + \frac{- 4 x}{5}$

Step 1.1.4.2.1.4

Move the negative in front of the fraction.

$y > \frac{7}{5} - \frac{4 x}{5}$

Step 1.1.4.2.1.5

Reorder $\frac{7}{5}$ and $- \frac{4 x}{5}$ .

$y > - \frac{4 x}{5} + \frac{7}{5}$

Step 1.2

Reorder terms.

$y > - (\frac{4}{5} x) + \frac{7}{5}$

Step 1.3

Remove parentheses.

$y > - \frac{4}{5} x + \frac{7}{5}$

Step 2

Use the slope-intercept form to find the slope and y-intercept.

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Step 2.1

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = - \frac{4}{5}$

$b = \frac{7}{5}$

Step 2.2

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

Slope: $- \frac{4}{5}$

y-intercept: $(0, \frac{7}{5})$

Slope: $- \frac{4}{5}$

y-intercept: $(0, \frac{7}{5})$

Step 3

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $- \frac{4}{5} x + \frac{7}{5}$ .

$y > - \frac{4}{5} x + \frac{7}{5}$

Step 4