To find an equivalent equation for w, we start with the initial equations provided. We know:
- Initial equation: 2x²y + 24 = w
- Another form provided: w = 8x²y + 2
To find an equivalent equation, we can set 2x²y + 24 equal to 8x²y + 2.
So, we will rewrite the equation:
2x²y + 24 = 8x²y + 2
Now, let’s solve for w:
- First, we will rearrange the equation:
2x²y + 24 – 2 = 8x²y
- Which simplifies to:
2x²y + 22 = 8x²y
- Next, we isolate terms involving x²y:
22 = 8x²y – 2x²y
- This combines to:
22 = 6x²y
- So we can express w as:
w = 6x²y + 22
Thus, the equivalent equation to find w is:
- 2x²y + 24 = w
- or
- w = 6x²y + 22
This shows different ways to express the same relationship, which is crucial when dealing in equations as it gives multiple paths to the same solution.