Solve the following inequality. Write the answer in interval notation.
4-x/x-10 is greater than or equal to 0
4-x/x-10 is greater than or equal to 0
-
Given (4 - x)/(x - 10) ≥ 0.
(i) The fraction on the left side is undefined for x = 10. (This is an open circle on the number line.)
(ii) Solving (4 - x)/(x - 10) = 0 yields 4 - x = 0
==> x = 4. (This is a closed circle on the number line, since we have "≥" and not ">".)
-------------------
So, the real number line is broken into three pieces (draw it!):
(i) For x < 4, note that (4 - x)/(x - 10) < 0 [try x = 0 for example].
(ii) For 4 < x < 10, note that (4 - x)/(x - 10) > 0 [try x = 5].
(iii) For x > 10, note that (4 - x)/(x - 10) < 0 [try x = 11].
Since the inequality is (4 - x)/(x - 10) ≥ 0, only 4 ≤ x < 10 is shaded.
So, the solution in interval notation is [4, 10).
I hope this helps!
(i) The fraction on the left side is undefined for x = 10. (This is an open circle on the number line.)
(ii) Solving (4 - x)/(x - 10) = 0 yields 4 - x = 0
==> x = 4. (This is a closed circle on the number line, since we have "≥" and not ">".)
-------------------
So, the real number line is broken into three pieces (draw it!):
(i) For x < 4, note that (4 - x)/(x - 10) < 0 [try x = 0 for example].
(ii) For 4 < x < 10, note that (4 - x)/(x - 10) > 0 [try x = 5].
(iii) For x > 10, note that (4 - x)/(x - 10) < 0 [try x = 11].
Since the inequality is (4 - x)/(x - 10) ≥ 0, only 4 ≤ x < 10 is shaded.
So, the solution in interval notation is [4, 10).
I hope this helps!