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How do you solve the inequality #abs(9-4x)<=0#?

Answer 1

Jameson Allen

To solve the inequality |9 - 4x| ≤ 0:

Since the absolute value of any real number is always non-negative, the absolute value of the expression 9 - 4x must be less than or equal to zero.
The only way for the absolute value of a real number to be less than or equal to zero is for the expression inside the absolute value to equal zero itself.
So, solve the equation 9 - 4x = 0:

9 - 4x = 0 -4x = -9 x = 9/4
Therefore, the solution to the inequality is x = 9/4.

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Answer 2

Ethan Adkins

This is a special case.

Since any absolute value, such as the one in our problem, is always greater than or equal to zero, the only solutions to #| 9 - 4x | <=0# occur when #9 - 4x = 0#. Simply solve this linear equation for x, and you will have the solution.

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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 the inequality #abs(9-4x)&lt;=0#?

How do you solve the inequality #abs(9-4x)<=0#?