The question seems to combine concepts related to mathematics and chemistry, and a structural formula appears required for different types of alkanols (alcohols). However, the provided context pertains primarily to solving a mathematical equation. Let's focus on the logical and mathematical portion to ensure we thoroughly address that aspect.
Given:
The equation provided is:
[tex]\[4 \cdot (18 - 3k) = 9 \cdot (k + 1)\][/tex]
1. Distribute Constants and Simplify Both Sides:
- Left side: [tex]\(4 \cdot (18 - 3k)\)[/tex]
[tex]\[72 - 12k\][/tex]
- Right side: [tex]\(9 \cdot (k + 1)\)[/tex]
[tex]\[9k + 9\][/tex]
Our equation thus simplifies to:
[tex]\[72 - 12k = 9k + 9\][/tex]
2. Combine Like Terms:
- Move all terms involving [tex]\(k\)[/tex] to one side of the equation:
[tex]\[72 - 12k - 9k = 9\][/tex]
[tex]\[72 - 21k = 9\][/tex]
- Move constant terms to the opposite side:
[tex]\[72 - 9 = 21k\][/tex]
[tex]\[63 = 21k\][/tex]
3. Solve for [tex]\(k\)[/tex]:
- Divide both sides by 21:
[tex]\[k = \frac{63}{21}\][/tex]
[tex]\[k = 3\][/tex]
Thus, the solution to [tex]\(k\)[/tex] is:
[tex]\[k = 3\][/tex]
4. Verification:
- Substitute [tex]\(k = 3\)[/tex] back into the original equation to ensure it balances:
[tex]\[4 \cdot (18 - 3 \cdot 3) = 9 \cdot (3 + 1)\][/tex]
[tex]\[4 \cdot 9 = 9 \cdot 4\][/tex]
[tex]\[36 = 36\][/tex]
This verifies that our solution of [tex]\(k = 3\)[/tex] is indeed correct.
In summary, the final step-by-step solution yielded the equation and confirmed that when solved, [tex]\(k\)[/tex] is:
[tex]\[k = 3\][/tex]
