Hi there,
This is the original inequality equation:
So, we first need to find the critical points of equality, and we can do that by switching the less than sign to an equal sign.
Now, we multiply both sides by x + 1:
Then, we multiply both sides by x - 1:
Next, we subtract x² from both sides:
After that, we solve for x. We do this by adding -x to both sides and dividing by 2. Doing so gives us x = 0, which is our first critical point. We need to find a few more critical points by testing x = -1 and x = 1. Here is how we do that:
<span>x = <span>−1 </span></span>(Makes left denominator equal to 0)<span>x = 1 </span>(Makes right denominator equal to 0)Check intervals in between critical points. (Test values in the intervals to see if they work.)<span>x <<span>−1 </span></span>(Doesn't work in original inequality)<span><span><span>−1 </span>< x </span><0 </span>(Works in original inequality)<span><span>0 < x </span>< 1 </span>(Doesn't work in original inequality)<span>x > 1 </span><span>(Works in original inequality)
Therefore, the answer to your query is
-1 < x < 0 or x > 1. Hope this helps and have a phenomenal day!</span>
Answer:
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Step-by-step explanation:
The simplified expressions are 2^-2 and 60^6
<h3>How to simplify the expressions?</h3>
<u>Expression (a)</u>
We have:
2^3 * 2^-5
Apply the product law of indices
2^3 * 2^-5 = 2^(3 - 5)
Evaluate the difference
2^3 * 2^-5 = 2^-2
<u>Expression (b)</u>
We have:
(60^2)^3
Apply the power law of indices
(60^2)^3 = 60^(2 * 3)
Evaluate the product
(60^2)^3 = 60^6
Hence, the simplified expressions are 2^-2 and 60^6
Read more about expressions at:
brainly.com/question/723406
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In this problem, it is important to take note that the number of numbers to be utilized isn't specified so it can be up to a thousand numbers. It wasn't also specified if repeating of numbers is allowed or not. So with those taken into consideration and the condition presented in mind, the numbers that can give you 8 when added and 30 when multiplied are 2, 3, 5, -1, and another -1. The derivation from this is mainly from factorization and a little bit of logic.
here is the solution.
2 x 3 x 5 x -1 x -1 = 30
6 x 5 x -1 x -1 = 30
30 x -1 x -1 = 30
-30 x -1 = 30
30 = 30
2 + 3 + 5 + -1 + -1 = 8
5 + 5 + -1 + -1 = 8
10 + -1 + -1 = 8
9 + -1 = 8
8 = 8