### Home > CC3MN > Chapter 2 > Lesson 2.1.7 > Problem2-68

2-68.

Read the Math Notes boxes in this lesson and for Lesson 2.1.5. Then examine the work below that shows one way to simplify the expression $3x+8+(x+10)$. Decide which property was used for each step.

Expression

What property was used?

$3x+8+(x+10)$

Original expression

$(3x+8+x)+10$

a.

$(3x+x+8)+10$

b.

$(4x+8)+10$

$4x+(8+10)$

c.

$4x+18$

What is the property used to rearrange parentheses with addition?

In part (b), some terms are moved. Why is this a legal move?

The answers are filled in below.

Expression

What property was used?

$3x+8+(x+10)$

Original expression

$(3x+8+x)+10$

$(3x+x+8)+10$

(b). Commutative Property

$(4x+8)+10$

$4x+(8+10)$
$4x+18$