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How do you graph and solve #|2x - 5| = |2x + 5|#?

Answer 1

Avery Alexander

#|2x-5|=|2x+5|#, if and only if x = 0. The graph is the origin.

Of course, as #x to +-oo, |2x-5|/|2x+5| to 1.#

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Answer 2

Genesis Allen

To graph and solve the equation ( |2x - 5| = |2x + 5| ), follow these steps:

Split the equation into two cases based on the absolute value expressions: Case 1: ( 2x - 5 = 2x + 5 ) Case 2: ( 2x - 5 = -(2x + 5) )
Solve each case separately for ( x ): Case 1: ( 2x - 5 = 2x + 5 ) ( 2x - 2x = 5 + 5 ) ( 0 = 10 ) (This is a contradiction, so Case 1 has no solution.)

Case 2: ( 2x - 5 = -(2x + 5) ) ( 2x - 5 = -2x - 5 ) ( 2x + 2x = -5 + 5 ) ( 4x = 0 ) ( x = 0 )
Verify the solution by substituting ( x = 0 ) into the original equation: ( |2(0) - 5| = |2(0) + 5| ) ( |0 - 5| = |0 + 5| ) ( |-5| = |5| ) ( 5 = 5 ) (This verifies that ( x = 0 ) is indeed a solution.)
Plot the solution ( x = 0 ) on a number line.

Therefore, the solution to the equation ( |2x - 5| = |2x + 5| ) is ( x = 0 ), and its graph consists of a single point at ( x = 0 ) on the number line.

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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.