Use the figure below to answer questions 8-10.
Point B is the midpoint of Segment A C..
A line segment with three points on it. From left to right, the points are labeled A, B, and C.
8. a. Find x if AB = 4x and BC = 2x + 10.
b. Use the answer for x to find the values of AB and BC.
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Use the figure below to answer questions 8-10. Point B is the midpoint of Segment A C..
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To find the value of x, we need to use the fact that point B is the midpoint of segment AC. This means that the length AB is equal to the length BC.
a. To find x, we can set up an equation using the given lengths AB = 4x and BC = 2x + 10:
AB = BC
4x = 2x + 10
Now, we can solve for x by subtracting 2x from both sides of the equation:
4x - 2x = 2x + 10 - 2x
2x = 10
Dividing both sides of the equation by 2, we get:
x = 5
b. Now that we have the value of x, we can substitute it back into the expressions for AB and BC:
AB = 4x = 4(5) = 20
BC = 2x + 10 = 2(5) + 10 = 20
Therefore, the values of AB and BC are 20.
To find the value of x, we can set up the equation using the given information: AB = 4x and BC = 2x + 10.
Since point B is the midpoint of segment AC, we know that AB is equal to BC.
Therefore, we can set up the equation AB = BC:
4x = 2x + 10
Simplifying the equation, subtract 2x from both sides:
4x - 2x = 2x + 10 - 2x
2x = 10
Divide both sides by 2:
x = 10 / 2
x = 5
Now that we have found the value of x, we can use it to find the lengths of AB and BC.
a. AB = 4x = 4 * 5 = 20
BC = 2x + 10 = 2 * 5 + 10 = 10 + 10 = 20
b. Therefore, the values of AB and BC are both 20 units.