Question

Point D lies between points P and Q. PD = 3x+6. DQ = 2x+4. PQ = 30. What is the measure of PD

Answer 1

The measure of PD is 18 units.

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.

`PQ=PD+DQ`

`PQ=3x+6+2x+4`

Combine like terms.

`PQ=(3x+2x)+(6+4)`

`PQ=5x+10`

The length of PQ is 30.

`30=5x+10`

Subtract 10 from both sides.

`30-10=5x+10-10`

`20=5x`

Divide both sides by 5.

`4=x`

The value of x is 4.

The measure of PD is

`PD=3x+6=3(4)+6\Rightarrow 12+6=18`

Therefore the measure of PD is 18 units.

Answer 2

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