Question

J is the midpoint of CT if CJ=5x-3 and JT=2x+21 find CT

Answer 1

Since J is the midpoint of the CT segment, then:

`\begin{gathered} CJ=JT \\ 5x-3=2x+21 \end{gathered}`

Now, you can solve the equation for x:

`\begin{gathered} 5x-3=2x+21 \\ \text{ Add 3 from both sides of the equation} \\ 5x-3+3=2x+21+3 \\ 5x=2x+24 \\ \text{ Subtract 2x from both sides of the equation} \\ 5x-2x=2x+24-2x \\ 3x=24 \\ \text{ Divide by 3 from both sides of the equation} \\ (3x)/(3)=(24)/(3) \\ x=8 \end{gathered}`

Replace the value of x into the equation for segment CJ or segment JT to find out what its measure is. For example in the equation of the segment CJ:

`\begin{gathered} CJ=5x-3 \\ x=8 \\ CJ=5(8)-3 \\ CJ=40-3 \\ CJ=37 \end{gathered}`

Finally, you have

`\begin{gathered} CJ=37 \\ CJ=JT \\ 37=JT \\ \text{ Then} \\ CT=CJ+JT \\ CT=37+37 \\ CT=74 \end{gathered}`

Therefore, the measure of the segment CT is 74.