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Talja [164]
3 years ago
13

Solve each absolute value equation or inequality and choose the correct answer from the choices provided

Mathematics
1 answer:
NeX [460]3 years ago
7 0

<u>Answers:</u>


1) |x|+5=18  

If we want to solve equations with absolute values we must know we have to find the solution for both positive and negative values. This is because positive and negative values have a positive absolute value.

In a mathematical form this is:

<h2>For any positive number a, the solution to |x|=a is: </h2><h2>|x|=a or |x|=-a </h2>

In this case we have to clear |x| first:

|x|=18-5

|x|=13

This means x=13 or x=-13

Therefore, the answer is B

2) |x+3|

In the case of inequalities we have the following statement:  

<h2>For any positive value of a: </h2><h2>|x| is equivalent to -a </h2><h2>|x|>a is equivalent to x or x>a </h2>

Where x may be a normal variable or an algebraic expression, as the expression in this exercise.

According to the explained above:

 

|x+3| is equivalent to -5< x+3

This means we have to solve the inequality for both cases.

<u> Case 1: </u>

x+3

x

x

<u>Case 2: </u>

x+3>-5

x>-5-3

x>-8

Then, x or x>-8

3) |-3n|-2=4

|-3n|=4+2

|-3n|=6

This means |-3n|=6 or |-3n|=-6

<u>Case 1: </u>

-3n=6

n=-\frac{6}{3}

n=-2

<u>Case 2: </u>

-3n=-6

n=\frac{-6}{-3}

n=2

Then, the answer is A: n=-2 or n=2


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