Question

are the expressions $5(m + 1) - 1$ and $2(2m + 2) + m$ equivalent? show why or why not.
simplify the first expression $5(m + 1) - 1$.
$5(m + 1) - 1 = \square m + ?$

Explanation:

Step1: Apply Distributive Property

Use the distributive property \(a(b + c)=ab + ac\) to expand \(5(m + 1)\). So, \(5(m + 1)=5\times m+5\times1 = 5m + 5\).

Step2: Simplify the Expression

Now, substitute back into the original expression \(5(m + 1)-1\). We have \(5m + 5-1\). Combine the constant terms: \(5 - 1 = 4\). So the simplified expression is \(5m+4\).

Answer:

The coefficient of \(m\) is \(5\) and the constant term is \(4\), so \(5(m + 1)-1=\boldsymbol{5}m+\boldsymbol{4}\).