Question

Find x if S is the midpoint of segment RT and RS = 2x+4 and ST = 5x-5.

a) x=3
b) x=4
c) x=7
d) x=12

Answer 1

To determine the value of x when S is the midpoint of RT, we equate the lengths of RS and ST given as 2x+4 and 5x-5, respectively. After performing algebraic operations, we find that the value of x is 3.

Step-by-step explanation:

If S is the midpoint of segment RT, the lengths of segments RS and ST are equal. We are given RS equals 2x+4 and ST equals 5x-5. To find the value of x, we set 2x+4 equal to 5x-5 because RS = ST.

Here is the equation: 2x + 4 = 5x - 5.

To solve for x, we'll first subtract 2x from both sides of the equation:
4 = 3x - 5. Next, we add 5 to both sides: 9 = 3x. Finally, divide both sides by 3 to isolate x: x = 3.

Therefore, the correct value of x when S is the midpoint of segment RT and given the lengths of segments RS and ST is 3.