Solve
X + 1/x – 2 ≥ 3
I know you have to subtract the 3 from both sides to get the zero on right of the inequality sign. I don't understand how to make one fraction after I do this.
with brackets,
(x + 1)/(x – 2) ≥ 3
following your idea ...
(x + 1)/(x – 2) - 3 ≥
we need a common denominator of x-2
(x+1 -3x+6)/(x+1) ≥ 0
(-2x+7)(/(x-2) ≥ 0
so I see 2 critical values, x=7,2 and x=2
splitting the number line into 3 sections,
a) less than 7/2
b) between 7/2 and 2
c) greater than 2
pick any arbitrary value in each region, we don't actually have to evaluate it, just worry about the + or -
a) let x = 0 then +/- , does not work
b) let x = 3, then +/+ > 0 , YES
c) let x = 10, then -/+ , no way
so only the numbers between 7/2 and 2 work, but remember x cannot be 2 or else we are dividing by zer.
so the solution is
7/2 ≤ x < 2 , x is a real number
Thank you very much, you have been a great help!!!
To solve the inequality X + 1/x - 2 ≥ 3, you're correct that we need to subtract 3 from both sides of the inequality in order to isolate the variable on one side.
Starting with the original inequality:
X + 1/x - 2 ≥ 3
Subtracting 3 from both sides:
X + 1/x - 5 ≥ 0
Now, let's combine the X and 1/x terms to create a single fraction. To do this, we need to find a common denominator. In this case, the common denominator is x. To get a common denominator, multiply the first term (X) by x/x and the second term (1/x) by 1/1:
(X * x + 1/x * 1) / x ≥ 0
Now, simplify the numerator by expanding:
(X * x + 1) / x ≥ 0
At this point, the inequality is in the form of a single fraction.