Question:|x-2|, if x > 5 simplify without the absolute value sign
1 answer:
Answer:
x - 2, if x > 5
Step-by-step explanation:
The vertical lines either side of the expression mean absolute value.
The absolute value of a number is its <u>positive numerical value</u>.
if x > 5 then as 5 > 2, the values inside the vertical lines will always be positive. Therefore, we can disregard the absolute value.
Therefore:
x - 2, if x > 5
To find the range (output values) of the expression, substitute x = 5 into the expression:
⇒ 5 - 2 = 3
Therefore, |x - 2| > 3, if x > 5
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Answer:
Step-by-step explanation:
We'll call the 2 numbers x and y. Starting with the last part of that first sentence "one number is 10 times the other number" can be written, in algebraic form:
y = 10x
Now on to the first statement about the numbers: "twice their sum" is 2(x + y) and "equals their product" is = xy. Putting that all together:
2(x + y) = xy and we know that y = 10x so
2(x + 10x) = x(10x) and
and
and
x(10x - 22) = 0 so
x = 0 or 10x - 22 = 0 which makes
x equal to
So x = 2.2 and y = 22.