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∣x−7∣=∣2x−8∣ (there are 2 solutions for the positive one and the negative)

1 Answer

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Answer:

x = 1, x = 5

Explanation:

|x−7|=|2x−8| ==> there are 2 ways to simplify this equation:

1. x - 7 = 2x - 8

2. -(x - 7) = 2x - 8

Let's first solve equation 1:

x - 7 = 2x - 8

-7 = x - 8 ==> subtract x on both sides

x - 8 + 8 = -7 + 8 ==> add 8 on both sides

x = 1 ==> simplify

Now let's solve equation 2:

-(x - 7) = 2x - 8

-x - (-7) = 2x - 8 ==> distribute the negative sign to x and -7

-x + 7 = 2x - 8 ==> subtracting a negative number is equivalent to adding a

positive number

7 = 3x - 8 ==> add x on both sides

15 = 3x ==> add 8 on both sides

x = 5 ==> divide 3 on both sides

Hence, the answers are x = 1 and x = 5.

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