Question
Solve each absolute value inequality. Graph the solution
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. Then we plot the graph on the x- axis, or the real line R in such a way that the graph satisfies the value of x from both the cases.
The correct answer is: Combining the above two solutions, we get -4 < x < 4
Step by step solution:
The given inequality is
2|x|-1 < 7
Adding 1 both sides, we get
2|x|< 7 + 1
Dividing by 2, we get
|x| < 4
We use the definition of 
, which is
For,
,
We have
Multiplying on both sides, we have
Or
For, 
,
We have
That is
Combining the above two solutions, we get
We plot the above inequality on the real line.
The points -4 and 4 are not included in the graph.
Adding 1 both sides, we get
Dividing by 2, we get
We use the definition of
, which is ,We have
Multiplying on both sides, we have
,We have
That is
Combining the above two solutions, we get
We plot the above inequality on the real line.
The points -4 and 4 are not included in the graph.
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’.
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Solve - 0.85t - 0.85t -3.9 = - 8.15
An equation in which highest power of any variable is always 1 is known as a Linear equation.
We will simplify the given equation and find the value of t.
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We will simplify the given equation and find the value of t.
Solve 1.037x + 0.02X + 25 = 30.285
An equation in which highest power of any variable is always 1 is known as a Linear equation.
We will simplify the given equation and find the value of x.
Solve 1.037x + 0.02X + 25 = 30.285
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We will simplify the given equation and find the value of x.
different from solving 
× √21x3 × 4√7x2
