Question

If m > n, which inequalities must be true? Check all that apply. m + 2.1 > n + 2.1 m - (-4) > n -(-4) m + 3 > n-3 16.5 + m > 16.5 + n 1 m > n + 2 9 + m > 6 + 1

Answer 1

Let's begin by listing out the information given to us:

m > n

We will proceed to solve the inequalities given as shown below:

`\begin{gathered} If\colon m>n \\ \\ m+2.1>n+2.1 \\ \text{Subtract ''2.1'' from both sides, we have:} \\ m>n \\ m+2.1>n+2.1\Rightarrow m>n \\ \therefore m+2.1>n+2.1(TRUE) \\ \\ m-(-4)>n-\mleft(-4\mright) \\ \Rightarrow m+4>n+4 \\ \text{Subtract ''4'' from both sides, we have:} \\ m>n \\ m+4>n+4\Rightarrow m>n \\ \therefore m+4>n+4(TRUE) \\ \\ m+3>n-3 \\ \text{Subtract '3'' from both sides, we have:} \\ m>n-3-3\Rightarrow m>n-6 \\ m>n-6\\e m>n \\ \therefore m+3>n-3(FALSE) \\ \\ \end{gathered}`

The last three choices are below:

`\begin{gathered} 16.5+m>16.5+n \\ \text{Subtract ''16.5'' from both sides, we have:} \\ m>n \\ 16.5+m>16.5+n\Rightarrow m>n \\ \therefore16.5+m>16.5+n(TRUE) \\ \\ m>n+2​ \\ m>n+2​\\e m>n \\ \therefore m>n+2​(FALSE) \\ \\ \\ \end{gathered}`

The inequalities marked as TRUE are the inequalities that apply