The solution interval for x is x ∈ (-1/4 , ∞)
An inequality shows the relationship of a non-equal comparison between two numbers or mathematical expressions.
Here, we are given two inequalities
x/4 > -1 and -4x - 4 < -3
Let us take the first equation
x/4 > -1
⇒ x > 4(-1)
x > -4
Now, the second equation
-4x - 4 < -3
-4x < -3 + 4
-4x < 1
Now since we are dividing both sides by a negative number, that is 4, the sign of the inequality will be reversed,
x > 1/-4
x > -1/4
Thus, we get x > -4 and x > -1/4
This means that all values of x greater than -1/4 will satisfy.
Thus, x ∈ (-1/4 , ∞)
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Answer:
for question 15, it is true
and for question 12 the order goes as
-2, - 1 3/4, - 1 1/2, -1/2, -1/4
Step-by-step explanation:
Answer:
A(x+2)(x-3)(x+6) where A is a constant.
If you want to change the order in that multiplication you can.
Read answer for my options on what your answer could look like.
Let me know the choices or if you have any questions.
Step-by-step explanation:
It says which like you have choices...
But I can give you several polynomials with those zeros.
By factor theorem if you have -6 is a zero then x+6 is a factor.
By factor theorem if you have -2 is a zero then x+2 is a factor.
By factor theorem if you have 3 is a zero then x-3 is a factor.
So a polynomial with those factors I mentioned is:
(x+6)(x+2)(x-3)
or
4(x+6)(x+2)(x-3)
or
-12(x+6)(x+2)(x-3)
or
1.4(x+6)(x+2)(x-3)
and so on....
I guess you could also say
4(x+6)(x+2)(x-3)^3.
It didn't say it had to have this multiplicity of 1.
Anyways I think you are probably looking for an option that says something like this:
A(x+6)(x+2)(x-3)
where A is a constant.
Keep in mind multiplication is commutative so it could be written as
A(x+2)(x-3)(x+6) or something similar to that.