Question
What is the value of x in 
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
First, we simplify the inequality and then solve it by considering the two cases.
The correct answer is: Combining the above two solutions, we get -50/4<x<9
Step by step solution:
The given inequality is
We use the definition of 
, which is
For, 
,
We have
Simplifying, we get
Adding 7 on both sides, we get
Dividing by -4 on both sides, we have
Or
For, 
,
We have
Subtracting 7 from both sides, we get
Dividing by 4 throughout,
Combining the above two solutions, we get
We use the definition of
, which is ,We have
Simplifying, we get
Adding 7 on both sides, we get
Dividing by -4 on both sides, we have
,We have
Subtracting 7 from both sides, we get
Dividing by 4 throughout,
Combining the above two solutions, we get
The given inequality contains only one variable. So, the graph is plotted on one dimension, which is the real line. 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’.
Related Questions to study
Rewrite expression to remove perfect square factors other than 1 in radicand. √32x4y3
Rewrite expression to remove perfect square factors other than 1 in radicand. √32x4y3
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.
