Question

If m and n can be any integers such that n<4 and 4m - 3n < 20, which of following is the solution set for m?A m <7.25B m 50C. m < 8D. m 2 7.25m 20

Answer 1

If we multiply the inequality n<4 by 3 we get the following:

`(n<4)\cdot3=3n<12`

Now, on the next inequality we have the following:

`\begin{gathered} 4m-3n<20 \\ \Rightarrow4m<20+3n \end{gathered}`

By transitive property, we have:

`\begin{gathered} 3n<12 \\ 4m<20+3n<20+12=32 \\ 4m<32 \\ \Rightarrow m<(32)/(4)=8 \\ m<8 \end{gathered}`

therefore, the solution set for m is m<8