2 1 practice absolute value equations and inequalities answer key


Asked by admin @ in Mathematics viewed by 355 People


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

1. [X]+5=18
A.5 or-5
B.13 or-13
C. 18 or -18
D. 23 or-23
2. [x+3]<5
A. -8
B. -2
C. 3
D.-3
3. [-3n] -2=4
A. 2 or -2
B. 3 or -3
C. 4 or -4
D. 6 or -6

Answered by admin @



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





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