If RS = 3x + 1, ST = 2x - 2, And RT = 64. What is the value of x.

3x + 1 + 2x - 2 = 64

5x -1 = 64 (the combined length of both line segments)
5x = 65
x = 13

To find the value of x, we can use the given information about the lengths of the line segments RS, ST, and RT.

We know that RS + ST = RT (by the Triangle Inequality Theorem). Let's substitute the given expressions for RS and ST into the equation:

(3x + 1) + (2x - 2) = 64

Now, we can simplify and solve for x:

5x - 1 = 64
5x = 65
x = 65/5
x = 13

Therefore, the value of x is 13.

To find the value of x, we will use the information given about the lengths of RS, ST, and RT.

We know that RS + ST = RT, based on the segment addition postulate.

Let's substitute the given values into the equation:

(3x + 1) + (2x - 2) = 64

Simplifying the equation, we combine like terms:

5x - 1 = 64

Next, add 1 to both sides of the equation to isolate the variable term:

5x - 1 + 1 = 64 + 1

Simplifying further:

5x = 65

To solve for x, divide both sides of the equation by 5:

5x/5 = 65/5

This simplifies to:

x = 13

Therefore, the value of x is 13.