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4x=6-|4x-3/2| hi I need help to find this answer

User Tae
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1 Answer

4 votes

Answer:

x = 15/16

Explanation:

Before we can begin solving, we need to isolate everything inside the absolute value brackets:

(4x = 6 - |4x - 3/2|) - 6

(4x - 6 = - |4x - 3/2|) / -1

-4x + 6 = |4x - 3/2|

Because we have an absolute value equation, we make two separate equations with a positive and negative answer since any positive number and its negative equivalent have the same absolute value (e.g. |5| = 5 and |-5| = 5):

  • Note that for any absolute value equation, there's a chance to have 0 solutions, 1 solution, or 2 solutions

Positive answer:

  • Also note that for the positive answer, we don't change anything on the left-hand side.

(-4x + 6 = 4x - 3/2) + 4x

(6 = 8x - 3/2) + 3/2

(15/2 = 8x) / 8

(15/2 = 8x) * 1/8

15/16 = x

Thus, one of the answers for x is 15/16.

Negative answer:

  • For the negative answer, we must multiply the left-hand side by -1:

-1(-4x + 6) = 4x - 3/2

(4x - 6 = 4x - 3/2) - 4x

-6 = -3/2

Because the equation is not true, there is only one answer for the absolute value equation.

User Merus
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