Final answer:
To find the value of x, set the expressions for SM (5x-10) and MT (3x+2) equal to each other and solve for x. The value of x is 6.
Step-by-step explanation:
The question seeks to determine the value of x when given two expressions for the segments SM and MT, where M is the midpoint of ST. By definition, SM and MT must be equal since M is the midpoint, so we can set their expressions equal to each other and solve for x:
SM = MT
5x - 10 = 3x + 2
Solving for x involves combining like terms and isolating x on one side of the equation:
5x - 3x = 2 + 10
2x = 12
Divide both sides by 2 to find x:
2x / 2 = 12 / 2
x = 6
Therefore, the value of x is 6.