Given:
Point P is on line segment OQ.
PQ=x+7,OP=4x-10,and OQ=4x.
To find:
The numerical length of OQ.
Solution:
Since, point P is on line segment OQ, so by segment addition property, we get
[tex]OQ=OP+PQ[/tex]
[tex]4x=(4x-10)+(x+7)[/tex]
[tex]4x=(4x+x)+(7-10)[/tex]
[tex]4x=5x-3[/tex]
[tex]4x-5x=-3[/tex]
[tex]-x=-3[/tex]
[tex]x=3[/tex]
The value of x is 3.
Now,
[tex]OQ=4x[/tex]
Putting x=3, we get
[tex]OQ=4(3)[/tex]
[tex]OQ=12[/tex]
Therefore, the numerical length of OQ is 12 units.
