Algebra Examples

$3 x - 2 y < 6$

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

$3 x$ from both sides of the inequality.

$- 2 y < 6 - 3 x$

Step 1.1.2

Divide each term in

$- 2 y < 6 - 3 x$ by

$- 2$ and simplify.

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Step 1.1.2.1

Divide each term in

$- 2 y < 6 - 3 x$ by

$- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 y}{- 2} > \frac{6}{- 2} + \frac{- 3 x}{- 2}$

Step 1.1.2.2

Simplify the left side.

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Step 1.1.2.2.1

Cancel the common factor of

$- 2$ .

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Step 1.1.2.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} > \frac{6}{- 2} + \frac{- 3 x}{- 2}$

Step 1.1.2.2.1.2

Divide

$y$ by

$1$ .

$y > \frac{6}{- 2} + \frac{- 3 x}{- 2}$

Step 1.1.2.3

Simplify the right side.

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Step 1.1.2.3.1

Simplify each term.

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Step 1.1.2.3.1.1

Divide

$6$ by

$- 2$ .

$y > - 3 + \frac{- 3 x}{- 2}$

Step 1.1.2.3.1.2

Dividing two negative values results in a positive value.

$y > - 3 + \frac{3 x}{2}$

Step 1.2

Rearrange terms.

$y > \frac{3 x}{2} - 3$

Step 1.3

Reorder terms.

$y > \frac{3}{2} x - 3$

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

$y = m x + b$ .

$m = \frac{3}{2}$

$b = - 3$

Step 2.2

The slope of the line is the value of

$m$ , and the y-intercept is the value of

$b$ .

Slope:

$\frac{3}{2}$

y-intercept:

$(0, - 3)$

Slope:

$\frac{3}{2}$

y-intercept:

$(0, - 3)$

Step 3

Graph a dashed line, then shade the area above the boundary line since

$y$ is greater than

$\frac{3}{2} x - 3$ .

$y > \frac{3}{2} x - 3$

Step 4