Solve the absolute value inequality:?

Question

Problem 1.

|8n+4| < -4

Problem 2.

|4x+1| > 0

Answer 1

#1 no solution. absolute value is always positive. (never less than -4)

#2 all real numbers except -1/4. this absolute value will always be strictly greater than zero (positive) unless it is equal to zero. this inequality calls for strictly greater than, not greater than or equal to.

Answer 2

Problem 1 has no solution because the left side of the equation must be at least zero by the definition of absolute value.

Problem 2: the zero makes the absolute value kind of pointless.
4x+1 > 0 or -(4x+1) > 0
4x > -1 or -4x > 1
x > -1/4 or x < -1/4 (change signs when dividing by neg)
x > -1/4 or x < -1/4
x =/= -1/4

Answer 3

There is no answer for problem one since |8n+4| is an absolute value; it has only positive results.

for problem 2:

x can be all real numbers, since the function is in the modulus mode, and so even a negative answer will turn into a positive answer, which is definitely greater than 0. x cannot be only -1/4 since the function will equal zero, whereas it should be greater than it.

Answer 4

once you've absolute value lower than some thing, then it truly is a 'between' reality as you position it. for instance once you've |x| < 5, this suggests x < 5 And -x < 5 which suggests x > -5. So -5 < x < 5 (between). once you've absolute value better than some thing, then it is an 'Or' reality. once you've |x| > 5, this suggests x > 5 Or -x > 5 which suggests x < -5. So x > 5 OR x < -5. contained in the examples I gave above, you could imagine of absolute value because the area from the muse. So if the area from the muse is lower than some thing, then it must be between (or And, similar ingredient). And if the area from the muse is larger than some thing, it must be Or. you'll see this quite in case you draw the determination line out for the example I gave above. i'm hoping this facilitates you.

Answer 5

first
|8n+4| >0
so first problem have no answer
second
|4x+1| > 0(we know |f(x)|>=0 )
so 4x+1=0
x=-1/4
answer is R-[-1/4]

Answer 6

|8n + 4| < -4
This problem has no solution because you can't have a negative value involving absolute values.

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|4x + 1| > 0
4x + 1 > 0 or 4x + 1 < 0
4x > -1 or 4x < -1
x > (-1/4) or x < (-1/4)

ANS : x > (-1/4) or x < (-1/4)

Answer 7

ans for prob1: No solution
bec. LHS is +ve and RHS is -ve
prob2 : x = any real number
bec the statement is always true irrespective of the value of x