Algebra Examples

$\frac{2}{5} x - \frac{1}{5} y \geq 0$

Step 1

Solve for $y$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$\frac{2 x}{5} - \frac{1}{5} y \geq 0$

Step 1.1.2

Combine $y$ and $\frac{1}{5}$ .

$\frac{2 x}{5} - \frac{y}{5} \geq 0$

Step 1.2

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

$- \frac{y}{5} \geq - \frac{2 x}{5}$

Step 1.3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- y \geq - 2 x$

Step 1.4

Divide each term in $- y \geq - 2 x$ by $- 1$ and simplify.

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Step 1.4.1

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

$\frac{- y}{- 1} \leq \frac{- 2 x}{- 1}$

Step 1.4.2

Simplify the left side.

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Step 1.4.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} \leq \frac{- 2 x}{- 1}$

Step 1.4.2.2

Divide $y$ by $1$ .

$y \leq \frac{- 2 x}{- 1}$

Step 1.4.3

Simplify the right side.

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Step 1.4.3.1

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

$y \leq - 1 \cdot (- 2 x)$

Step 1.4.3.2

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

$y \leq - (- 2 x)$

Step 1.4.3.3

Multiply $- 2$ by $- 1$ .

$y \leq 2 x$

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 $y = m x + b$ .

$m = 2$

$b = 0$

Step 2.3

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

Slope: $2$

y-intercept: $(0, 0)$

Slope: $2$

y-intercept: $(0, 0)$

Step 3

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

$y \leq 2 x$

Step 4