Algebra Examples

2 x - y > 4

$2 x - y > 4$

Step 1

Write in

y = m x + b

$y = m x + b$ form.

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Step 1.1

Solve for

y

$y$ .

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Step 1.1.1

Subtract

2 x

$2 x$ from both sides of the inequality.

- y > 4 - 2 x

$- y > 4 - 2 x$

Step 1.1.2

Divide each term in

- y > 4 - 2 x

$- y > 4 - 2 x$ by

- 1

$- 1$ and simplify.

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Step 1.1.2.1

Divide each term in

- y > 4 - 2 x

$- y > 4 - 2 x$ by

- 1

$- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

\frac{- y}{- 1} < \frac{4}{- 1} + \frac{- 2 x}{- 1}

$\frac{- y}{- 1} < \frac{4}{- 1} + \frac{- 2 x}{- 1}$

Step 1.1.2.2

Simplify the left side.

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Step 1.1.2.2.1

Dividing two negative values results in a positive value.

\frac{y}{1} < \frac{4}{- 1} + \frac{- 2 x}{- 1}

$\frac{y}{1} < \frac{4}{- 1} + \frac{- 2 x}{- 1}$

Step 1.1.2.2.2

Divide

y

$y$ by

1

$1$ .

y < \frac{4}{- 1} + \frac{- 2 x}{- 1}

$y < \frac{4}{- 1} + \frac{- 2 x}{- 1}$

y < \frac{4}{- 1} + \frac{- 2 x}{- 1}

$y < \frac{4}{- 1} + \frac{- 2 x}{- 1}$

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

4

$4$ by

- 1

$- 1$ .

y < - 4 + \frac{- 2 x}{- 1}

$y < - 4 + \frac{- 2 x}{- 1}$

Step 1.1.2.3.1.2

Move the negative one from the denominator of

\frac{- 2 x}{- 1}

$\frac{- 2 x}{- 1}$ .

y < - 4 - 1 \cdot (- 2 x)

$y < - 4 - 1 \cdot (- 2 x)$

Step 1.1.2.3.1.3

Rewrite

- 1 \cdot (- 2 x)

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

- (- 2 x)

$- (- 2 x)$ .

y < - 4 - (- 2 x)

$y < - 4 - (- 2 x)$

Step 1.1.2.3.1.4

Multiply

- 2

$- 2$ by

- 1

$- 1$ .

y < - 4 + 2 x

$y < - 4 + 2 x$

y < - 4 + 2 x

$y < - 4 + 2 x$

y < - 4 + 2 x

$y < - 4 + 2 x$

y < - 4 + 2 x

$y < - 4 + 2 x$

y < - 4 + 2 x

$y < - 4 + 2 x$

Step 1.2

Rearrange terms.

y < 2 x - 4

$y < 2 x - 4$

y < 2 x - 4

$y < 2 x - 4$

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

$y = m x + b$ , where

m

$m$ is the slope and

b

$b$ is the y-intercept.

y = m x + b

$y = m x + b$

Step 2.2

Find the values of

m

$m$ and

b

$b$ using the form

y = m x + b

$y = m x + b$ .

m = 2

$m = 2$

b = - 4

$b = - 4$

Step 2.3

The slope of the line is the value of

m

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

b

$b$ .

Slope:

2

$2$

y-intercept:

(0, - 4)

$(0, - 4)$

Slope:

2

$2$

y-intercept:

(0, - 4)

$(0, - 4)$

Step 3

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

y

$y$ is less than

2 x - 4

$2 x - 4$ .

y < 2 x - 4

$y < 2 x - 4$

Step 4