(50 ) the two triangles are similar. what is the value of x?

Place (3x + 1)/12, and (4x)/15    (Note: the bottom triangle's base is 12 + 3)

Set the two equal to each other

(3x + 1)/12 = (4x)/15

Cross multiply

15(3x +1)/12(12) = 12(4x)/15(15)

15(3x + 1) = 12(4x)

Distribute the 15 to the two terms in the parenthesis, and 12 to 4x

15(3x) = 45x
15(1) = 15
12(4x) = 48x

45x + 15 = 48x

Isolate the variable, subtract 45x from both sides

45x (-45x) + 15 = 48x (-45x)

15 = 48x - 45x

Simplify

15 = 3x

Isolate the x, divide 3 from both sides

15/3 = 3x/3

x = 15/3

x = 5

5 is your answer

hope this helps

With a continuous thought process.