If BC = 2x + 1, CD = 3x - 4 and BD = 22, find the value of x
Assuming the segment is labeled BCD, with C between B and D,
2x + 1 + 3x -4 = 22
5x = 25
x = 5
To solve for x, we can set up an equation by adding the lengths of BC and CD and then setting it equal to the length of BD.
BC = 2x + 1
CD = 3x - 4
Adding BC and CD:
BC + CD = (2x + 1) + (3x - 4)
Now we set this sum equal to the length of BD, which is 22:
BC + CD = 22
Substituting the values of BC and CD into the equation:
(2x + 1) + (3x - 4) = 22
Simplifying the equation:
2x + 1 + 3x - 4 = 22
Combining like terms:
5x - 3 = 22
Adding 3 to both sides of the equation:
5x = 25
Finally, to solve for x, divide both sides of the equation by 5:
x = 5
So the value of x is 5.