Points R, S, and T are collinear and S is between R and T.
Find x if RS = 8x + 4, ST = 4x + 8, and RT = 15x - 9.
Since points R, S, and T are collinear, the sum of their lengths should be equal to the length of the entire line segment:
RS + ST = RT
Substituting the given values:
8x + 4 + 4x + 8 = 15x - 9
Combining like terms:
12x + 12 = 15x - 9
Subtracting 12x and adding 9 to both sides:
12 = 3x - 9
Adding 9 to both sides:
21 = 3x
Dividing both sides by 3:
x = 7
Therefore, x is equal to 7.
To find x, we need to set up an equation. Since points R, S, and T are collinear, the sum of the lengths of RS and ST should equal the length of RT.
Given:
RS = 8x + 4
ST = 4x + 8
RT = 15x - 9
The equation can be set up as follows:
RS + ST = RT
Substituting the given values:
(8x + 4) + (4x + 8) = 15x - 9
Now, let's solve the equation to find the value of x.
First, we combine like terms on the left side of the equation:
8x + 4 + 4x + 8 = 15x - 9
12x + 12 = 15x - 9
Next, we need to isolate the x term on one side of the equation. Let's start by moving the 15x term to the right side and the 12 term to the left side:
12x - 15x = -9 - 12
-3x = -21
To solve for x, we need to divide both sides of the equation by -3:
-3x / -3 = -21 / -3
x = 7
Therefore, x equals 7.