Final answer:
To find the value of x for the line segments RS, ST, and RT, we form the equation 3x + 1 + 2x - 2 = 64 by combining RS and ST to equal RT, simplify it to 5x - 1 = 64, and then solve to get x = 13.
Step-by-step explanation:
To solve for the value of x when RS = 3x+1, ST = 2x-2, and RT = 64, we can first understand that RS + ST equals RT because they are segments on the same line. Given this, we can write the equation 3x + 1 + 2x - 2 = 64. This is a straightforward linear equation with only one unknown, x, which makes it the best way to find x without needing additional information.
Now, we simplify and rearrange the equation:
- Combine like terms: 3x + 2x +1 - 2 = 64
- Simplify the equation: 5x -1 = 64
- Add 1 to both sides: 5x = 65
- Divide by 5: x = 13
By solving this equation, we find that x = 13.