What is the value of x? Justify each step.
AC=32
2x 6x+8
.__________________._________________.
A B C
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AB + BC = AC a.__________________________
2x+6x + 8 =32 b. __________________________
8x + 8 =32 c. __________________________
8x =24 d. __________________________
X =3 e. __________________________
Online, “*” is used to indicate multiplication to avoid confusion with “x” as an unknown.
2*6x+8?
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To find the value of x in the given equation, we can follow these steps:
a. Start by using the fact that the sum of the lengths of two segments is equal to the length of the third segment (AB + BC = AC). In this case, AB corresponds to 2x, BC corresponds to 6x + 8, and AC is given as 32. So we have the equation 2x + (6x + 8) = 32.
b. Simplify the equation by combining like terms. The equation becomes 8x + 8 = 32. This step involves adding the coefficients (2x + 6x = 8x) and the constant terms (0 + 8 = 8).
c. Next, subtract 8 from both sides of the equation to isolate the variable term. This step helps to solve for x. The equation becomes 8x = 24.
d. Divide both sides of the equation by the coefficient of x, which in this case is 8. This step helps to solve for x. The equation becomes x = 3.
e. Finally, we have found the value of x. The value of x is 3.
By following these steps, you can justify each step in the process of finding the value of x.