What is the value of x? Justify each step.
AC= 32
AB+BC= AC a.
2x+ 6x +8 =32 b.
8x+8= 32 c.
8x= 24 d.
x= 3 e.
In this problem, we are given that AC = 32. We are also given that AB + BC = AC.
a. Since AB + BC = AC, we substitute the values for AB and BC from the given information in the question.
2x + 6x + 8 = 32
b. We combine like terms to simplify the equation.
8x + 8 = 32
c. We subtract 8 from both sides of the equation to isolate the variable term on one side.
8x = 24
d. We divide both sides by 8 to solve for x.
x = 3
Therefore, the value of x is 3, and each step was justified using the rules of algebra.