Solve 5-2x > 4, then represent on a number line
1 answer:
Answer: x < 1/2 or x < 0.5
The graph is below
=========================================================
There are two ways to solve this
Method 1
5 - 2x > 4
-2x > 4-5
-2x > -1
x < -1/(-2) .... note the inequality sign flips
x < 1/2
x < 0.5
The inequality sign flips whenever we divide both sides by a negative number.
----------------------
Method 2
5 - 2x > 4
5 - 2x+2x > 4+2x
5 > 4+2x
4+2x < 5
2x < 5-4
2x < 1
x < 1/2
x < 0.5
----------------------
To graph this on a number line, we'll plot an open hole at 1/2 or 0.5 on the number line. Then we shade to the left to represent all values smaller than 1/2 = 0.5
The open hole signals that 0.5 itself is NOT part of the solution set.
See the diagram below.
You might be interested in
<h3>Answer:</h3>
x=2
<h3>Solution:</h3>- In order to isolate x, we should first of all take the square root of both sides.
- If we take the square root of the left-hand side, we will get
- How about the right-hand side? Well, we should take the square root of the numerator (9) and the denominator (4)
- So we have
- Move -1/2 to the right:
- x=2
Hope it helps.
Do comment if you have any query.
Answer:
We want to find:
Here we can use Stirling's approximation, which says that for large values of n, we get:
Because here we are taking the limit when n tends to infinity, we can use this approximation.
Then we get.
Now we can just simplify this, so we get:
And we can rewrite it as:
The important part here is the exponent, as n tends to infinite, the exponent tends to zero.
Thus: