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3 years ago

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Consider the absolute value inequality: |x - 6| > 20. Will the graph of the solutions to the inequality result in an "and" or

an "or" inequality? Without solving to find the exact solutions, explain

1 answer:

Dmitrij [34]3 years ago

3 0

Step-by-step explanation:

Case 1 : |x| > a, => x > a or x < -a

Case 2 : |x| < a, => -a < x < a

Since this question follows Case 1, we will have an "or" inequality.

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What is an equation of the line that passes through the points (-6, -2) and

den301095 [7]

Answer:

The equation of line is: $\mathbf{4x-3y=-18}$

Step-by-step explanation:

We need to find an equation of the line that passes through the points (-6, -2) and (-3, 2)?

The equation of line in slope-intercept form is: $y=mx+b$

where m is slope and b is y-intercept.

We need to find slope and y-intercept.

Finding Slope

Slope can be found using formula: $Slope=\frac{y_2-y_1}{x_2-x_1}$

We have $x_1=-6,y_1=-2, x_2=-3, y_2=2$

Putting values and finding slope

$Slope=\frac{2-(-2)}{-3-(-6)}\\Slope=\frac{2+2}{-3+6} \\Slope=\frac{4}{3}$

So, we get slope: $m=\frac{4}{3}$

Finding y-intercept

Using point (-6,-2) and slope $m=\frac{4}{3}$ we can find y-intercept

$y=mx+b\\-2=\frac{4}{3}(-6)+b\\-2=4(-2)+b\\-2=-8+b\\b=-2+8\\b=6$

So, we get y-intercept b= 6

Equation of required line

The equation of required line having slope $m=\frac{4}{3}$ and y-intercept b = 6 is

$y=mx+b\\y=\frac{4}{3}x+6$

Now transforming in fully reduced form:

$y=\frac{4x+6*3}{3} \\y=\frac{4x+18}{3} \\3y=4x+18\\4x-3y=-18$

So, the equation of line is: $\mathbf{4x-3y=-18}$

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