Question

Solve for x. Please show work.

Answer 1

First exercise:
`x=7`

Second exercise:
`x=2`

Explanation:

Acording to the Intersecting Secants Theorem the products of the segments of two secants that intersect each other outside a circle, are equal.

Based on this, in order to solve the first exercise and the second exercise, we can write the following expressions and solve for "x":

First exercise:

`(5)(5+x)=6(6+4)\\\\25+5x=60\\\\5x=60-25\\\\x=(35)/(5)\\\\x=7`

Second exercise:

`(4)(4+x)=3(3+5)\\\\16+4x=24\\\\4x=24-16\\\\x=(8)/(4)\\\\x=2`