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How do you solve #|2x-3|<2#?

Answer 1

Eva Abramson

The solution is #x in (1/2,5/2)#

The disparity is

#|2x-3|<2#

Consequently,

If #2x-3<2#, then #2x-3>-2#.

The initial formula provides

#2x<2+3#

#x<5/2#

The subsequent formula provides

#2x>-2+3#

#x>1/2#

Putting the #2# solutions together

#x in (1/2,5/2)#

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Answer 2

Genesis Allen

#1/2 < x <5/2#

#"Type-II inequality: |x|< a#"

# "Always have solutions of the form" #

#-a < x < a#

#rArr-2< 2x-3 < 2#

# "add 3 to all three intervals" #

2xcancel(-3)cancel(color(red)(+3))<2color(red)(+3)#

#rArr1< 2x <5#

# "divide all three intervals by 2" #

#rArr1/2 < x < 5/2#

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Answer 3

Avery Alexander

To solve the inequality |2x - 3| < 2: 1. Set up two cases: a) 2x - 3 < 2 b) 2x - 3 > -2 2. Solve each case separately for x: a) 2x - 3 < 2 Add 3 to both sides: 2x < 5 Divide by 2: x < 2.5 b) 2x - 3 > -2 Add 3 to both sides: 2x > 1 Divide by 2: x > 0.5 3. Combine the solutions from both cases: x < 2.5 and x > 0.5 4. Write the combined solution in interval notation: (0.5, 2.5)

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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 #|2x-3|&lt;2#?

How do you solve #|2x-3|<2#?