Yis the midpoint of xz. if xz= 8x-2 and yz= 2x+1 ,find x

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 1 = x.

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