Question

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

Answer 1

Answers:

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:

For any positive number $a$, the solution to $|x|=a$ is:

$|x|=a$ or $|x|=-a$

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:  

For any positive value of $a$:

$|x|$ is equivalent to $-a$

$|x|>a$ is equivalent to $x$ or $x>a$

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.

Case 1:

$x+3$

$x$

$x$

Case 2:

$x+3>-5$

$x>-5-3$

$x>-8$

Then, $x$ or $x>-8$

3) $|-3n|-2=4$

$|-3n|=4+2$

$|-3n|=6$

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

Case 1:

$-3n=6$

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

$n=-2$

Case 2:

$-3n=-6$

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

$n=2$

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