How do you solve #abs(5x+3)=abs(2x-1)#?

Answer 1

Case 1: Both Absolute Values are positive

#5x + 3 = 2x - 1#
#3x = -4#
#x = -4/3#

Case 2: The left absolute value is negative

#-(5x + 3) = 2x - 1#
#-5x - 3 = 2x - 1#
#-7x = 2#
#x = -2/7#

Case 3: The right absolute value is negative

#5x + 3 = -(2x - 1)#
#5x + 3 = -2x + 1#
#7x = -2#
#x = -2/7#

As you can see, whether the absolute value on right is negative and the other positive or the absolute value on left is negative and the other positive, both scenarios will give the same result.

Let's just check our solutions to make sure none are extraneous.

#|5(-4/3) + 3| =^? |2(-4/3) - 1|#
Doing all the fractal operations on this, you will find that this, as well as the other solution, #x = -2/7#, work in the original equation.
Hence, our solution set is #{x = -2/7, -4/3}#.

Hopefully this helps!

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Answer 2

To solve |5x + 3| = |2x - 1|, you'll need to consider two cases: when the expressions inside the absolute value bars are positive and when they are negative.

  1. For when 5x + 3 and 2x - 1 are both positive: 5x + 3 = 2x - 1

  2. For when 5x + 3 and 2x - 1 are both negative: -(5x + 3) = -(2x - 1)

Solve each equation separately to find the values of x.

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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.

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.

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.

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.

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