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How do you solve absolute value inequality #-3abs(2x-5)<9#?

Answer 1

Normally we would consider the two cases #(2x-5)# is negative and #(2x-5)# is positive or zero, separately and evaluate each case for restrictions on the value of #x#.

However, in this case #(-3)abs(2x-5)<9# can be re-written as #abs(2x-5)> -3# (by dividing both sides by #(-3)# and reversing the inequality)

#abs(2x-5) >=0 >-3# for all values of #x# (based on the definition of absolute value

so the solution to the given inequality is #x epsilon (-oo,+oo)#

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Answer 2

Abigail Allen

To solve the absolute value inequality -3|2x - 5| < 9, you would first isolate the absolute value term, then divide both sides by the coefficient of the absolute value. Finally, you would solve the resulting inequality.

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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 absolute value inequality #-3abs(2x-5)&lt;9#?

How do you solve absolute value inequality #-3abs(2x-5)<9#?