Question

Hey! Can I have a simple explanation and a value for x?

Answer 1

Hello from MrBillDoesMath

Answer:

    x   = 6

Discussion:

We are told the triangles are similar so corresponding parts have equal ratios . In our case this becomes

(5x-2)/7x = (3x+2)/5x

and we need to solve for "x". Multiply both sides by x

(5x-2)/7x*x  = (3x+2)/5x*x =>

(5x -2)/7 = (3x+2)/5                    ( as x/x = 1)

Multiply both sides by 35 ( = 7 * 5)

(5x-2)/ 7  * (7*5) =  (3x +2 )/ 5 * (7*5)  =>

(5x-2) * 5 = (3x +2) * 7 =>

25x -10 = 21x + 14        =>          (subtract 21x from both sides)

(25x - 21x) - 10 =  14 =>              (simplify)

4x - 10  = 14  =>                           (add 10 to both sides)

4x = 14 + 10  =>                  

4x = 24  =>

x = 6

Thank you,

Mr. B