Question

Use the commutative property to write an equivalent expression to 4g + 13, and show that they are equivalent for g = 10 and g = 2. Complete the statements.

If you change the order of the terms you can create the equivalent expression
.

After substituting 10 for g, the expressions are
and
.

After substituting 2 for g, the expressions are 4(2) + 13 and 13 + 4(2).

The expressions are equivalent because they both have a value of
when g = 10 and a value of
when g = 2.

Answer 1

If you change the order of the terms you can create the equivalent expression **13 + 4g**.

After substituting 10 for g, the expressions are **4(10) + 13** and **13 + 4(10)**.

After substituting 2 for g, the expressions are **4(2) + 13** and **13 + 4(2)**.

The expressions are equivalent because they both have a value of **53** when g = 10 and a value of **21** when g = 2.

**Step-by-step calculations:**

1. For \( g = 10 \):
- \( 4g + 13 = 4(10) + 13 = 40 + 13 = 53 \)
- \( 13 + 4g = 13 + 4(10) = 13 + 40 = 53 \)

2. For \( g = 2 \):
- \( 4g + 13 = 4(2) + 13 = 8 + 13 = 21 \)
- \( 13 + 4g = 13 + 4(2) = 13 + 8 = 21 \)

Thus, both expressions yield the same results for the given values of \( g \).