Understanding
What is absolute value?
Absolute value of a number is the number's distance from zero.
How do you solve ∣x∣=3
the solutions are x=- 3 or 3
Give a real-life example of absolute value.
What is Distance problems?
Distance between any two numbers on the number line can be found by simply subtracting them in either order and taking the absolute value.
What is an equation?
Is a mathematical sentence stating that two expressions are equal.
What is the absolute value of −7?
7
Absolute value represents the distance from zero on a number line, regardless of direction. So, whether a number is positive or negative, its absolute value is always positive.
Therefore, |-7| = 7.
|x| + 2 =5
first subtract 2 from both sides to get ∣x∣=3. The solutions are x=−3 or = 3.
How can absolute value help in distance calculations?
Can absolute value of any expression be a negative?
No there is no solution.
What are solutions?
Values of variables that make an equation true.
What does | x | = 5 mean?
∣x∣=5 means that | x | can be either 5 or −5.
|x| = 4
x = 4 or -4
What is the importance of absolute value in graphing?
Absolute value is important in graphing because it creates a V-shape on the graph, indicating all values that are at a certain distance from a point.
What is isolate the absolute value?
Isolate is applying the addition and multiplication properties of equality.
What is addition property?
states that if the same term is added to or subtracted from both sides of an equation , the two sides of the equation will remain equal.
How do you represent an absolute value equation?
An absolute value equation is typically represented using vertical bars around the expression.
For example, if you want to represent the absolute value of x, you would write it as |x|.
x/2 - 7/10 = x/5 - 5/2
= -6
Explain how absolute value is used in temperature differences.
Absolute value is used in temperature differences to describe how far temperatures are from a reference point, regardless of whether they are above or below that point.
When clearing fractions what do you need to find first?
The LCD
What is multiplication property?
States that if each side of an equation is multiplied or divided by the same number , the two sides of the equation will remain equal.
Explain why absolute value is always non-negative.
Absolute value is always non-negative because it measures distance.
-|x| - 3 = 1
No solution
Describe a scenario where you would need to find the absolute value.
A scenario where you would need to find the absolute value is when calculating how far a player is from the starting line in a race, regardless of whether they are ahead or behind.
When clearing decimals what do you need to do first?
Multiply both sides of the by the same power.
What is contradiction?
The equation is false no matter what the value is substituted for the variable.