Question
Solve ![vertical line 3 x minus 6 vertical line equals 12](data:image/png;base64,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)
The cruising speed of Kennedy's boat is 25 mi/h. She plans to cruise at this speed for the distances shown in the diagram. What equation models the number of hours x that Kennedy will travel ?
![](data:image/png;base64,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)
a. What are the minimum and maximum number of hours kennedy will travel ?
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
![vertical line x vertical line equals open curly brackets table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell negative x comma x less than 0 end cell row cell x comma x greater or equal than 0 end cell end table close](data:image/png;base64,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)
So, we will get two cases in the solution of the given equation. We simplify the equation as much as possible and then apply the above definition to get the value of x.
For 2nd part, we will construct an equation which models the situation with the help of the concept of absolute value.
The correct answer is: x=2.8, 3.6
Step by step solution:
The given equation is
|3x - 6| = 12
Using the definition of absolute value,
![vertical line x vertical line equals open curly brackets table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell negative x comma x less than 0 end cell row cell x comma x greater or equal than 0 end cell end table close](data:image/png;base64,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)
We get two possibilities,
For 3x - 6 < 0,
|3x - 6| = -(3x - 6) = 12
Simplifying, we get
-3x + 6 = 12
Subtracting 6 both sides, we have
-3x = 12 - 6 = 6
Dividing throughout by -3, we get
x = -2
For 3x - 6 ≥ 0,
|3x - 6| = 3x - 6 = 12
Adding 6 both sides, we get
3x = 12 + 6 = 18
Dividing by 3 throughout, we get
x = 6
Hence, we get two values of x satisfying the given equation,
x = -2, 6
Given,
The number of hours travelled = x
Cruising speed of Kennedy’s boat = 25 mi/h
Distance she plans to travel = 80 10 mi
We know,
Speed= ![fraction numerator space D i s tan c e over denominator space T i m e end fraction](data:image/png;base64,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)
The above equation can be rewritten as
Distance=Speed × Time
We form an equation in terms of distance travelled by the boat.
From the above relation, we have
Total distance travelled by the boat = 25x mi
Thus, the equation representing the given situation is
|25x -80| = 10
We solve the above equation to get two values of x, which will be the minimum and maximum values of x.
Using the definition of absolute value,
![vertical line x vertical line equals open curly brackets table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell negative x comma x less than 0 end cell row cell x comma x greater or equal than 0 end cell end table close](data:image/png;base64,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)
We get two possibilities,
For 25x - 80 < 0,
|25x - 80 |= -(25x - 80) = 10
Simplifying, we get
-25x + 80 = 10
Subtracting 80 both sides, we have
-25x = 10 - 80 = -70
Dividing throughout by -25, we get
x =
= 2.8
For 25x - 80 ≥ 0,
|25x - 80| = 25x - 80 = 10
Adding 80 both sides, we get
25x = 10 + 80 = 90
Dividing by 25 throughout, we get
x =
= 3.6
Hence, we get two values of x satisfying the given equation,
x=2.8, 3.6
Thus,
Maximum number of hours Kennedy travels = 3.6 hours
Minimum number of hours Kennedy travels = 2.8 hours
Using the definition of absolute value,
We get two possibilities,
Simplifying, we get
Subtracting 6 both sides, we have
Dividing throughout by -3, we get
Adding 6 both sides, we get
Dividing by 3 throughout, we get
Hence, we get two values of x satisfying the given equation,
Given,
The number of hours travelled = x
Cruising speed of Kennedy’s boat = 25 mi/h
Distance she plans to travel = 80 10 mi
We know,
The above equation can be rewritten as
Distance=Speed × Time
We form an equation in terms of distance travelled by the boat.
From the above relation, we have
Total distance travelled by the boat = 25x mi
Thus, the equation representing the given situation is
|25x -80| = 10
We solve the above equation to get two values of x, which will be the minimum and maximum values of x.
Using the definition of absolute value,
We get two possibilities,
Simplifying, we get
Subtracting 80 both sides, we have
Dividing throughout by -25, we get
Adding 80 both sides, we get
Dividing by 25 throughout, we get
Hence, we get two values of x satisfying the given equation,
Thus,
Maximum number of hours Kennedy travels = 3.6 hours
Minimum number of hours Kennedy travels = 2.8 hours
Absolute value of a variable has many uses in mathematics. Geometrically, the absolute value of a number may be considered as its distance from zero regardless of its direction. The symbol |.| is pronounced as ‘modulus’. We read |x| as ‘modulus of x’ or ‘mod x’.