Question

H, J, and K are collinear points with J as a midpoint of H and K. HJ = 4x + 6 and HK = 44.

Find the value of x.

Answer 1

To find the value of x, we used the midpoint property, set up an equation based on the given lengths, and solved for x, arriving at x = 4.

Step-by-step explanation:

The student is tasked with finding the value of x based on the given information that points H, J, and K are collinear with J being the midpoint and given distances HJ and HK. Since J is the midpoint, HJ is equal to JK. Therefore, the equation for HJ which is 4x + 6 is also applicable for JK. To find HK, we add HJ and JK which gives us 2(4x + 6). This sum should be equal to the given HK distance of 44.

Following the steps to solve for x:

1. Write the equation based on the midpoint property: 2(4x + 6) = 44.
2. Distribute 2 into the parentheses: 8x + 12 = 44.
3. Subtract 12 from both sides: 8x = 32.
4. Divide by 8 to solve for x: x = 4.