Question

simplify the expression: $7v + 2 + 12 + 2v$
options: 23, 23v, 9 + 14v, 9v + 14

Explanation:

Step1: Combine like terms for variables

We have \(7v\) and \(2v\) as like terms (terms with the variable \(v\)). To combine them, we add their coefficients. The coefficient of \(7v\) is \(7\) and the coefficient of \(2v\) is \(2\). So, \(7v + 2v=(7 + 2)v\).
Calculating \(7+2\) gives \(9\), so \(7v + 2v = 9v\).

Step2: Combine like terms for constants

We have \(2\) and \(12\) as constant terms (terms without a variable). To combine them, we add the numbers: \(2+12 = 14\).

Step3: Combine the results from Step1 and Step2

Now we combine the simplified variable term (\(9v\)) and the simplified constant term (\(14\)) to get the simplified expression: \(9v+14\).

Answer:

\(9v + 14\)