Question

If RG=7x+3, GQ=3x+13, and RQ=56, then find the value for x, RQ, and GQ.

Answer 1

First, we'll write an equation using only the segments on the line. So:
RG+GQ= RQ
Since the segments of the line RQ are made up of RG and GQ, we will add RG and GQ together and set that equal to RQ.
Now, we'll plug in the numbers that correspond with the segments. 
So put 7x+3 in place of RG, and 3x+13 in place of GQ. Then set those equal to 56, which replace RQ. Your equation should now be:
7x+3+3x+13=56
Step 2: Combine like terms
10x+16=56
Step 3: Subtract 16 from each side
10x+16=56
       -16 -16
-------------------
10x=40
Step 4: Divide both sides by 10
$\frac{10}{10}=\frac{40}{10}$
Step 5: Reduce
$\frac{40}{10}$$= 4$

Now since x=4, just plug in the x value to find the length of segment RG and GQ.
RG= 7x+3
Step 2: Plug in value
RG= 7(4)+3
Step 3: Solve
RG= 28+3
So, RG=31
Next, GQ
GQ= 3x+13
Do the same as you did for finding RG:
GQ= 3(4)+13
GQ=12+13
GQ=25

So, here are all your answers:
x= 4 
RG= 31
GQ= 25
(You can also check to see if your answer is right by plugging in the actual value of RG and GQ and setting it equal to RQ. 31+25= 56)