Algebra Examples

$24 + 6 y \leq 5 x$

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

Subtract $24$ from both sides of the inequality.

$6 y \leq 5 x - 24$

Step 1.1.2

Divide each term in $6 y \leq 5 x - 24$ by $6$ and simplify.

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Step 1.1.2.1

Divide each term in $6 y \leq 5 x - 24$ by $6$ .

$\frac{6 y}{6} \leq \frac{5 x}{6} + \frac{- 24}{6}$

Step 1.1.2.2

Simplify the left side.

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Step 1.1.2.2.1

Cancel the common factor of $6$ .

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Step 1.1.2.2.1.1

Cancel the common factor.

$\frac{6 y}{6} \leq \frac{5 x}{6} + \frac{- 24}{6}$

Step 1.1.2.2.1.2

Divide $y$ by $1$ .

$y \leq \frac{5 x}{6} + \frac{- 24}{6}$

Step 1.1.2.3

Simplify the right side.

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Step 1.1.2.3.1

Divide $- 24$ by $6$ .

$y \leq \frac{5 x}{6} - 4$

Step 1.2

Reorder terms.

$y \leq \frac{5}{6} x - 4$

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 $y = m x + b$ .

$m = \frac{5}{6}$

$b = - 4$

Step 2.2

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

Slope: $\frac{5}{6}$

y-intercept: $(0, - 4)$

Slope: $\frac{5}{6}$

y-intercept: $(0, - 4)$

Step 3

Graph a solid line, then shade the area below the boundary line since $y$ is less than $\frac{5}{6} x - 4$ .

$y \leq \frac{5}{6} x - 4$

Step 4