B is between A and C.
AB=4x+3
BC=3x-2
AC=57
What is the value of x?
Solve the relationship AB + BC = AC
Substitute the appropriate algebraic expressions for the line lengths.
The result will be the equation
7x + 1 = 57
Solve that.
To find the value of x, we need to solve the equation AB + BC = AC using the given information.
We know that AB = 4x + 3, BC = 3x - 2, and AC = 57.
So, we can substitute these algebraic expressions into the equation AB + BC = AC:
(4x + 3) + (3x - 2) = 57
Simplifying the equation, we have:
7x + 1 = 57
Now we can solve for x.
Subtract 1 from both sides of the equation:
7x + 1 - 1 = 57 - 1
This simplifies to:
7x = 56
Divide both sides of the equation by 7:
(7x)/7 = 56/7
This further simplifies to:
x = 8
Therefore, the value of x is 8.