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

Answers:

1)  

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:

In this case we have to clear first:

This means or

Therefore, the answer is B

2)

In the case of inequalities we have the following statement:  

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

According to the explained above:

is equivalent to

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

Case 1:

Case 2:

Then, or

3)

This means or

Case 1:

Case 2:

Then, the answer is A: or

step-by-step explanation: h: (- 3, 6)

m: (1, - 2)

o: (7, 6)

r: (- 9, - 2)

midpoint of hm: (- 1, 2)

midpoint of or: (- 1, 2)

therefore, b is the midpoint of both diagonals bisect each other !

to prove the diagonals are perpendicular, show that the product of the slopes = - 1

b.-4 units

all you   do is count how many times you move