Question

which of the following are equivalent to the expression $6m + 4 - 2m + 9$? select all that apply.

a $4m + 5$

b $8m + 5$

c $8(m + 1) + 5$

d $4m + 13$

e $8m + 13$

f $4(m + 3) + 1$

Explanation:

Step1: Simplify the original expression

First, combine like terms in \(6m + 4 - 2m + 9\). The like terms for \(m\) are \(6m\) and \(-2m\), and the constant terms are \(4\) and \(9\).
For the \(m\)-terms: \(6m-2m = 4m\)
For the constant terms: \(4 + 9=13\)
So the original expression simplifies to \(4m + 13\) or we can also group \(6m-2m\) as \(8m - 4m\) (wait, no, let's re - check: \(6m-2m=4m\), and \(4 + 9 = 13\), so \(6m+4-2m + 9=4m + 13\). Also, we can rewrite \(6m-2m\) as \(8m-4m\)? No, better to do it step by step. Wait, another way: \(6m-2m=4m\), \(4 + 9 = 13\), so \(4m+13\). Also, we can factor differently: \(6m-2m=4m\), \(4 + 9 = 13\), so \(4m+13\). Now let's check each option:

Step2: Analyze Option A

Option A: \(4m + 5\). Since \(4m+13
eq4m + 5\) (because \(13
eq5\)), so A is incorrect.

Step3: Analyze Option B

Option B: \(8m+5\). \(4m + 13
eq8m+5\) (the coefficients of \(m\) and the constants are different), so B is incorrect.

Step4: Analyze Option C

Option C: \(8(m + 1)+5\). Expand \(8(m + 1)+5=8m+8 + 5=8m+13\). \(4m + 13
eq8m+13\) (coefficient of \(m\) is different), so C is incorrect.

Step5: Analyze Option D

Option D: \(4m+13\). This is the same as our simplified original expression, so D is correct.

Step6: Analyze Option E

Option E: \(8m + 13\). \(4m+13
eq8m + 13\) (coefficient of \(m\) is different), so E is incorrect.

Step7: Analyze Option F

Option F: \(4(m + 3)+1\). Expand \(4(m + 3)+1=4m+12 + 1=4m+13\). This is the same as our simplified original expression, so F is correct.

Answer:

D. \(4m + 13\), F. \(4(m + 3)+1\)