Question

determining equivalent expressions
which expression is equivalent to the expression 6h + 2?
○ (2 + 4h) + 2
○ (2 + 4h) + h
○ (1 + 5h) + 2
○ (2 + 5h) + h

Explanation:

Step1: Analyze each option

We need to simplify each option and check which one is equal to \(6h + 2\).

Step2: Simplify Option 1: \((2 + 4h)+2\)

Using the associative property of addition, we can remove the parentheses: \(2 + 4h+2\). Then combine like terms: \(4h+(2 + 2)=4h + 4\). This is not equal to \(6h + 2\).

Step3: Simplify Option 2: \((2 + 4h)+h\)

Remove the parentheses: \(2 + 4h+h\). Combine like terms: \(2+(4h + h)=2 + 5h\). This is not equal to \(6h + 2\).

Step4: Simplify Option 3: \((1 + 5h)+2\)

Remove the parentheses: \(1 + 5h+2\). Combine like terms: \(5h+(1 + 2)=5h + 3\). This is not equal to \(6h + 2\).

Step5: Simplify Option 4: \((2 + 5h)+h\)

Remove the parentheses: \(2 + 5h+h\). Combine like terms: \(2+(5h + h)=2 + 6h\), which is the same as \(6h + 2\) (by the commutative property of addition, \(2 + 6h=6h + 2\)).

Answer:

\((2 + 5h)+h\) (the fourth option)