What is the value of x? Justify each step.
AC=32
2x 6x+8 .__________________._________________.
A B C
Drawing not to scale
AB + BC = AC a.segment addition postulate
2x + 6x + 8 =32 b.substitution
8x + 8 = 32 c.simplification
8x = 24 d.addition property of equality
x = 3 e.multiplication property of equality
Is my proof reasoning correct?????
Yes, your proof reasoning is correct. Here is a breakdown of each step and justification:
a. Segment Addition Postulate: This postulate states that if three points A, B, and C are collinear and B is between A and C, then the length of AB plus the length of BC equals the length of AC.
b. Substitution: Since AB is represented as 2x and BC is represented as 6x + 8, you can substitute those expressions into the segment addition equation AB + BC = AC.
c. Simplification: By combining like terms, you simplify the equation 2x + 6x + 8 = 32 to 8x + 8 = 32.
d. Addition Property of Equality: Subtracting 8 from both sides of the equation, you get 8x = 24. This step follows the addition property of equality, which states that if a = b, then a + c = b + c.
e. Multiplication Property of Equality: Dividing both sides of the equation by 8, you get x = 3. This step follows the multiplication property of equality, which states that if a = b, then a * c = b * c.
Therefore, the value of x is 3.
Yes, your proof reasoning is correct. Allow me to explain each step:
a) The segment addition postulate states that if you have three points on a line, the distance between the first point and the third point is equal to the sum of the distances between the first and second points, and the second and third points.
b) In this step, you substituted the values of AB and BC into the equation, using the information given in the diagram. AB is represented as 2x, and BC is represented as 6x + 8. So, you substituted 2x + 6x + 8 for AB + BC.
c) By simplifying the equation, you combined like terms on the left side of the equation. Adding 2x and 6x, you get 8x. So, the equation becomes 8x + 8 = 32.
d) To isolate the variable x, you use the addition property of equality, which states that if you add the same number to both sides of an equation, the equality is preserved. In this step, you subtract 8 from both sides of the equation, which eliminates the +8 on the left side.
e) Finally, to solve for x, you use the multiplication property of equality, which states that if you multiply both sides of an equation by the same number, the equality remains true. Here, you divide both sides by 8, which isolates the variable x and gives you the value of x as 3.
Therefore, your proof reasoning is correct. Well done!
2x 6x + 8
.__________.__________.
A B C
this is a more accurate scale drawing