PD + DQ = PQ
Now, just plug in, combine like terms, and solve.
3x + 6 + 2x + 4 = 30
5x + 10 = 30
Subtract 10 from both sides to get variables on one side and constants on the other.
5x = 30 - 10
5x = 20
Divide by 5 to isolate the variable.
x = 20/5
x = 4
Now, plug in the x-value to find PD
PD = 3x + 6
= 3(4) + 6
12 + 6
18
PD = 18 units
Answer:
The measure of PD is 18 units.
Step-by-step explanation:
Given information: Point D lies between points P and Q. PD = 3x+6. DQ = 2x+4. PQ = 30.
The point D lies between points P and Q, so the segment PQ is the sum of line segments PD and DQ.
[tex]PQ=PD+DQ[/tex]
[tex]PQ=3x+6+2x+4[/tex]
Combine like terms.
[tex]PQ=(3x+2x)+(6+4)[/tex]
[tex]PQ=5x+10[/tex]
The length of PQ is 30.
[tex]30=5x+10[/tex]
Subtract 10 from both sides.
[tex]30-10=5x+10-10[/tex]
[tex]20=5x[/tex]
Divide both sides by 5.
[tex]4=x[/tex]
The value of x is 4.
The measure of PD is
[tex]PD=3x+6=3(4)+6\Rightarrow 12+6=18[/tex]
Therefore the measure of PD is 18 units.
