Question

If M is between G and T, MG = 2x + 1, MT = 3x + 3, and GT = 19, Then X = ___.MG = ___.MT = __.

Answer 1

We are given the following information

M is between G and T

MG = 2x + 1

MT = 3x + 3

GT = 19

Let us draw a sketch to better understand the problem

As you can see, the sum of MG and MT must be equal to the GT

Mathematically,

`\begin{gathered} GT=MG+MT \\ 19=(2x+1)+(3x+3) \end{gathered}`

Let us solve the above equation or x

`\begin{gathered} 19=2x+1+3x+3 \\ 19=2x+3x+1+3 \\ 19=5x+4 \\ 19-4=5x \\ 15=5x \\ (15)/(5)=x \\ 3=x \\ x=3 \end{gathered}`

So, the value of x is 3

`\begin{gathered} MG=2x+1 \\ MG=2(3)+1 \\ MG=6+1 \\ MG=7 \end{gathered}`
`\begin{gathered} MT=3x+3 \\ MT=3(3)+3 \\ MT=9+3 \\ MT=12 \end{gathered}`

Therefore, the required values are

x = 3

MG = 7

MT = 12