What is the value of x?

x = 5

which agrees with the first answer option listed

Step-by-step explanation:

Use the proportionality associated with similar triangles, considering that the larger triangle has sides:

x + (x+5) = 2 x + 5

and

(x+1) + (x-2) = 2 x - 1

and the smaller triangle:

x   and  (x-2)

The we build the following proportionality:

(2 x + 5) / x  = (2 x - 1) / (x - 2)

cross multiply to eliminate denominators:

(2 x + 5) (x - 2) = x (2 x - 1)

operate:

2 x^2 - 4 x + 5 x -10 = 2 x^2 - x

combine like terms:

2 x^2 + x -10 = 2 x^2 - x

subtract 2 x^2 from both sides:

x - 10 = - x

add x to both sides:

2 x  -10 = 0

add 10 to both sides

2 x= 10

divide both sides by 2:

x = 5

which agrees with the first answer option listed

arithmetic sequence: a sequnce in which the diffrence between any two consecutive terms is the same

step-by-step explanation:

inverse property is the answer

step-by-step explanation: