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.