Question

select the two expressions that are equivalent to the given expression remember that to simplify this experssion distribute a -1 to each term inside the second parentheses the combine like terms
(2x+2)-(3x+11)
a. -x+13
b. 2x-3x+2-11
c. -x+9
d. 2x-3x+2+11
e. -x-9
f. 5x+9
g. 5x+13

Answer 1

To simplify the expression \((2x + 2) - (3x + 11)\), we will follow the steps you've mentioned:

1. Distribute the \(-1\) to each term inside the second parentheses:
\[
(2x + 2) - (3x + 11) = 2x + 2 - 3x - 11
\]

2. Combine like terms:
\[
2x - 3x + 2 - 11 = -x - 9
\]

Now we have simplified the expression to \(-x - 9\).

Looking through the given options:

a. \(-x + 13\) (not equivalent)
b. \(2x - 3x + 2 - 11\) (this simplifies to \(-x - 9\), equivalent)
c. \(-x + 9\) (not equivalent)
d. \(2x - 3x + 2 + 11\) (this simplifies to \(-x + 13\), not equivalent)
e. \(-x - 9\) (equivalent)
f. \(5x + 9\) (not equivalent)
g. \(5x + 13\) (not equivalent)

The two expressions that are equivalent are **b** and **e**.