Question
Thato is solving the absolute value equation 
. What is the first step he should take?
Hint:
|x| is known as the absolute value of x. It is the non-negative value of x irrespective of its sign. The value of absolute value of x is given by
The symbol |.| is pronounced as ‘modulus’. We read |x| as ‘modulus of x’ or ‘mod x’.
The correct answer is: And for 3x ≥ 0, the equation becomes 3x-5=13
Step by step solution:
We cannot operate on |x| unless we determine if it is positive or negative. So first we need to eliminate the modulus.
To get rid of the modulus sign, we use the definition of absolute value of x, which is
The given equation is
The first step is to eliminate the mod with the definition above.
For 
, the equation reduces to
And for , the equation becomes
To find the solution of the given equation, Thato needs to solve these two equations.
The given equation is
The first step is to eliminate the mod with the definition above.
For
, the equation reduces toAnd for , the equation becomes
To find the solution of the given equation, Thato needs to solve these two equations.
This should always the first step while solving an equation which has a modulus value in it: to break it into two parts. Then it becomes easier to solve and interpret the equation.
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A road sign shows a Vehicle's speed as the vehicle passes.
a. The sign blinks for vehicles travelling within 
of the speed limit. Write and solve an absolute value inequality to find the minimum and maximum speeds of an oncoming vehicle that will cause the sign to blink.
b. Another sign blinks when it detects a vehicle travelling within 
of a 
speed limit. Write and solve an absolute value inequality to represent the speeds of the vehicles that cause the sign to blink.
|x|, which is pronounced "Mod x" or "Modulus of x," stands in for the absolute value of the variable x. The measure is the meaning of the Latin term "modulus." Common names for absolute value include numerical value and magnitude. The absolute value does not include the sign of the numeric value; it solely represents the numeric value. Any vector quantity's modulus is its absolute value and is always assumed to be positive.
Furthermore, absolute values express all quantities, including time, price, volume, and distance. Take the absolute value as an example: |+5| = |-5| = 5. The absolute value has no assigned sign. The formula to calculate a number's absolute value is |x| = x if it is greater than zero, |x| = -x if it is less than zero, and |x| = 0 if it is equal to zero.
A road sign shows a Vehicle's speed as the vehicle passes.
a. The sign blinks for vehicles travelling within of the speed limit. Write and solve an absolute value inequality to find the minimum and maximum speeds of an oncoming vehicle that will cause the sign to blink.
b. Another sign blinks when it detects a vehicle travelling within of a speed limit. Write and solve an absolute value inequality to represent the speeds of the vehicles that cause the sign to blink.
|x|, which is pronounced "Mod x" or "Modulus of x," stands in for the absolute value of the variable x. The measure is the meaning of the Latin term "modulus." Common names for absolute value include numerical value and magnitude. The absolute value does not include the sign of the numeric value; it solely represents the numeric value. Any vector quantity's modulus is its absolute value and is always assumed to be positive.
Furthermore, absolute values express all quantities, including time, price, volume, and distance. Take the absolute value as an example: |+5| = |-5| = 5. The absolute value has no assigned sign. The formula to calculate a number's absolute value is |x| = x if it is greater than zero, |x| = -x if it is less than zero, and |x| = 0 if it is equal to zero.
