If b is between A and C, find the value of "x" and BC.
AB=3(x+7),BC=2(x-3),and AC=50
AB + BC = 50 = 3x + 21 + 2x - 6
50 = 5x + 15
5x = 35
x = 7
To find the value of "x" and the length of BC, we can use the fact that b is between A and C. This means that the lengths of AB and BC, when added together, should be equal to the length of AC.
Given:
AB = 3(x + 7)
BC = 2(x - 3)
AC = 50
We can set up an equation using this information:
AB + BC = AC
Substituting the given expressions for AB and BC:
3(x + 7) + 2(x - 3) = 50
Now we can solve for "x":
3x + 21 + 2x - 6 = 50
5x + 15 = 50
5x = 35
x = 7
Therefore, the value of "x" is 7.
To find the length of BC:
BC = 2(x - 3)
BC = 2(7 - 3)
BC = 2(4)
BC = 8
Therefore, the length of BC is 8.