Question

Y is the midpoint of XZ. If XZ= 8x-2 and YZ= 2x+1 ,find x

Answer 1

Since Y is the midpoint of XZ, YZ will be half of the line. So, you can set up the equation 2(YZ) = XZ and substitute the values in to solve for x.

2(YZ) = XZ Substitute in the values
2(2x + 1) = 8x - 2 Use the Distributive Property
4x + 2 = 8x - 2 Add 2 to both sides
4x + 4 = 8x Subtract 4x from both sides
4 = 4x Divide both sides by 4
1 = x Switch the sides to make it easier to read
x = 1

Answer 2

The value of x is 1. To solve this problem you have to setup the equation like this: 2(2x + 1) = 8x -2. This equation works because since Y is the midpoint, if you double YZ then you get XZ. From the equation you use distributive property to multiply 2 by everything within the parenthesis now the equation should look like this: 4x+2 = 8x -2. Now you can add 2 to both sides making the equation look like this: 4x + 4 = 8x. Then you subtract 4x from each side turning the equation into something like this: 4=4x then you divide by 4 on each side getting your answer: 1 = x.