ACT Math : Absolute Value
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Example Question #673 : Arithmetic
Solve
All real numbers
No solutions
No solutions
Absolute values measure the distrance from the origin and is always positive, thus it can never be less than or equal to a negative number (unless a negative number is multiplied outside the absolute value). So the correct answer is no solutions.
Example Question #2 : How To Find Absolute Value
Absolute value is the key here. Absolute value means the number's distance from zero. So we must account for that. Therefore 
Example Question #1 : How To Find Absolute Value
What are the values of a and b, if any, where –a|b + 7| > 0?
a<0 and b = –7
a>0 and b not equal to 7
a<0 and b not equal to –7
a>0 and b not equal to –7
a<0 and b not equal to –7
The absolute value will always yield a positive, as long it is not zero. Therefore, b cannot equal –7. For the value to be positive, a must be a negative number.
Example Question #3 : How To Find Absolute Value
What is the absolute value of 19 – 36(3) + 2(4 – 87)?
–255
293
–168
168
255
255
19 – 36(3) + 2(4 – 87) =
19 – 108 + 2(–83) =
19 – 108 – 166 = –255
Absolute value is the non-negative value of the expression
Example Question #4 : Absolute Value
Solve for z where | z + 1 | < 3
1 < z < 3
–4 < z < 2
1 < z
–4 < z
z < 1 or z > 3x
–4 < z < 2
Absolute value problems generally have two answers:
z + 1 < 3 or z + 1 > –3 and subtracting 1 from each side gives z < 2 or z > –4 which bcomes –4 < z < 2
Example Question #2 : Absolute Value
Find the absolute value of the following when x = 2,
It is important to know that the absolute value of something is always positive so the absolute value of 
2 is your answer.
Example Question #2 : How To Find Absolute Value
Evaluate for 
Example Question #3 : How To Find Absolute Value
Evaluate for 
Substitute 0.6 for 
Example Question #2 : How To Find Absolute Value
Evaluate for 
Substitute 
Example Question #881 : Arithmetic
Which of the following sentences is represented by the equation
The sum of three and the absolute value of the sum of a number is three greater than the number.
The sum of three and the absolute value of the sum of a number is three less than the number.
The absolute value of the sum of a number and seven is three less than the number.
None of the other responses are correct.
The absolute value of the sum of a number and seven is three greater than the number.
The absolute value of the sum of a number and seven is three less than the number.
"The absolute value of the sum of a number and seven is three less than the number."
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