Answer:
The answer is x < 16.
Step-by-step explanation:
1) Remove parentheses.
2) Simplify x - 6 - 2 to x - 8.
3) Add 8 to both sides.
4) Simplify 8 + 8 to 16.
4) Switch sides.
<em><u>Therefor</u></em><em><u>,</u></em><em><u> </u></em><em><u>the</u></em><em><u> </u></em><em><u>answer</u></em><em><u> </u></em><em><u>is</u></em><em><u> </u></em><em><u>x</u></em><em><u> </u></em><em><u>></u></em><em><u> </u></em><em><u>16</u></em>.
Answer:
x - y is also a rational number. Hence satisfies the closure property.
Step-by-step explanation:
Closure property of subtraction states that for any two integers a and b, (a - b) must also be an integer.
Here x and y are rational numbers. so x - y must also be rational to satisfy the closure property.
Answer:
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Explanation:
We cannot have negative numbers under the square root, if we wanted the result to be some real number.
The stuff under the square root must be 0 or larger.
This means the x+2 must be 0 or larger.
Similarly, the 5-x must be 0 or larger. But wait, we cannot have 0 in the denominator (or else we have a division by zero error), so 5-x must be larger than 0.
5-x > 0
5-x+x > 0+x
5+0 > 0+x
5 > x
x < 5
Combine both and
to find the domain is
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Visual confirmation is shown below. I used Desmos which is a free graphing app.
The green curve is what we're after. It's between x = -2 and x = 5
We include -2, but exclude 5.
Take note of the closed endpoint at x = -2, and also the vertical asymptote at x = 5. The curve approaches this asymptote but never actually touches it. Think of an electric fence you can get closer to, but not actually touch.
