Kevin and Brittany write an equation to represent the following relationship, and both students solve their equation. Who found the correct equation and solution? Why is the other person incorrect?

6 times the difference of a number and 20 is the same as half the sum of 8 more than 8 times a number.

Kevin: 6(x − 20) =
1
2
(8x + 8) 6x − 120 = 4x + 4 6x − 120 − 4x = 4x + 4 − 4x 2x − 120 = 4 2x − 120 + 120 = 4 + 120 2x = 124
2x
2
=
124
2
x = 62 Brittany: 6(20 − x) =
1
2
(8x + 8) 120 − 6x = 4x + 4 120 − 6x − 4x = 4x + 4 − 4x 120 − 2x = 4 120 − 2x − 120 = 4 − 120 −2x = −116
−2x
−2
=
−116
−2
x = 58

The incorrect solution expressed the
difference of a number and 20 incorrectly
.
Kevin's
expression
20 − x
was correct.