Home > Algebra > Absolute Value Inequalities

How do you solve #abs(16-x)>=10#?

Answer 1

Nathan Axel

Solution: #x <= 6 or x >= 26# . In interval notation #(-oo , 6] uu [26 , oo)#

#|16-x| >=10 or 16-x >= 10 or -x >= -6 or x <= 6# OR #|16-x| >=10 or 16-x <= -10 or -x <= -26 or x >= 26#

Solution: #x <= 6 or x >= 26# . In interval notation #(-oo , 6] uu [26 , oo)# [Ans]

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Kennedy Adams

To solve the inequality (|16 - x| \geq 10), we consider two cases:

(16 - x \geq 10)
(16 - x \leq -10)

For Case 1: [16 - x \geq 10] [x \leq 6]

For Case 2: [16 - x \leq -10] [x \geq 26]

So, the solution to the inequality (|16 - x| \geq 10) is (x \leq 6) or (x \geq 26), which can be expressed in interval notation as ((- \infty, 6] \cup [26, +\infty)).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you solve #abs(16-x)&gt;=10#?

How do you solve #abs(16-x)>=10#?