Question

determining equivalent expressions
leon started to try to transform the expressions 6g + (g + 2) + 3 to determine if it is equivalent to the expression 6 + 7g. his work is shown below.
6g + (g + 2) + 3
(6g + g) + 2 + 3
7g + 2 + 3
associative property
combine like variable terms
are the expressions 6g + (g + 2) + 3 and 6 + 7g equivalent?

Explanation:

Step1: Simplify first expression

Simplify \(6g+(g + 2)+3\). Using associative property (grouping \(6g\) and \(g\), \(2\) and \(3\)): \((6g + g)+(2 + 3)\).

Step2: Combine like terms

Combine \(6g+g = 7g\) and \(2 + 3=5\), so first expression becomes \(7g + 5\).

Step3: Simplify second expression

Simplify \(6 + 7g\), which is \(7g+6\).

Step4: Compare expressions

\(7g + 5\) and \(7g+6\) have different constant terms (\(5
eq6\)), so they are not equivalent.

Answer:

No (the expressions \(6g+(g + 2)+3\) and \(6 + 7g\) are not equivalent)