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The equation |2x – 8| + 3 = 5 has 2 solutions. Those solutions are equal to the solutions to which of the following pairs of equations?

Question

The equation |2x – 8| + 3 = 5 has 2 solutions. Those solutions are equal to the solutions to which of the following pairs of equations?

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Solution

The equation |2x – 8| + 3 = 5 can be simplified to |2x – 8| = 2. This absolute value equation can be split into two separate equations: 2x - 8 = 2 and 2x - 8 = -2.

Solving these two equations gives:

2x - 8 = 2 --> 2x = 10 --> x = 5 2x - 8 = -2 --> 2x = 6 --> x = 3

So, the solutions to the original equation are x = 5 and x = 3.

Therefore, the solutions are equal to the solutions to the pair of equations 2x - 8 = 2 and 2x - 8 = -2.

This problem has been solved

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