Question
Write and solve an absolute value equation for the minimum and maximum times for an object moving at the given speed to travel the given distance.
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)
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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)
We will construct an equation which models the situation with the help of the concept of absolute value.
The correct answer is: Hence, we get two values of x satisfying the given equation, x=0.75, 1.25
Step by step solution:
Given,
Let the number of hours travelled be x
Speed of the object = 10 mi/h
Distance she plans to travel = 10 2.5 mi
We know,
The above equation can be rewritten as
We form an equation in terms of distance travelled by the boat.
From the above relation, we have
Total distance travelled by the boat = 10x mi
Thus, the equation representing the given situation is
|10x-10| = 2.5
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,
For 10x-10<0,
Simplifying, we get
- 10 x + 10 = 2.5
Dividing by 10 throughout, we get
Hence, we get two values of x satisfying the given equation,
x = 0.75, 1.25
Thus,
Maximum number of hours travelled = 1.25 hours
Minimum number of hours travelled = 0.75 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’.