Question

Point P is on line segment OQ. Given OQ = 4x + 2, PQ = 4x – 10, and

OP = 3x – 3, determine the numerical length of OQ.

Answer 1

OQ=5

Explanation:

The formula:

OP+PQ=OQ

Fill in the values for each segment using the values given:

3x-3+4x-10=4x+2

OP^ PQ^ OQ^

Simplify by adding like terms:

3x-3+4x-10=4x+2

7x-3-10=4x+2

add 13 to the right to isolate the variable:

7x-13=4x+2

+13 +13

7x=4x+15

subtract 4x to the left to isolate the variable:

7x=4x+15

-4x -4x

3x=15

Divide both sides by 3 to get the variable by itself:

3x=15

3 3

x=5 so OQ=5

Answer 2

22

Explanation:

Since, Point P is on line segment OQ.

`\therefore O - P - Q\\\\</p><p>\therefore OP + PQ = OQ\\\\</p><p>\therefore 3x - 3 + 4x - 10 = 4x + 2\\\\</p><p>\therefore 7x - 13 = 4x + 2\\\\</p><p>\therefore 7x - 4x = 2 + 13\\\\</p><p>\therefore 3x = 15\\\\</p><p>\therefore x = (15)/(3)\\\\</p><p>\huge \purple {\therefore x = 5} \\\\</p><p>OQ = 4x + 2 = 4* 5 + 2 = 20 + 2\\\\</p><p>\huge \orange {\boxed {OQ = 22}}`