Sure! Let's solve the equation [tex]\(4(18 - 3k) = 9(k + 1)\)[/tex] using algebraic methods step-by-step.
1. Distribute the constants inside the parentheses:
- For the left side: [tex]\(4(18 - 3k)\)[/tex]
- Distribute the 4: [tex]\(4 \cdot 18 - 4 \cdot 3k\)[/tex]
- This simplifies to: [tex]\(72 - 12k\)[/tex]
- For the right side: [tex]\(9(k + 1)\)[/tex]
- Distribute the 9: [tex]\(9 \cdot k + 9 \cdot 1\)[/tex]
- This simplifies to: [tex]\(9k + 9\)[/tex]
2. Set the simplified expressions equal to each other:
- [tex]\(72 - 12k = 9k + 9\)[/tex]
3. Combine like terms:
- Move all terms involving [tex]\(k\)[/tex] to one side and constants to the other side.
- Subtract [tex]\(9k\)[/tex] from both sides: [tex]\(72 - 12k - 9k = 9\)[/tex]
- This simplifies to: [tex]\(72 - 21k = 9\)[/tex]
- Next, isolate the term involving [tex]\(k\)[/tex]:
- Subtract 72 from both sides: [tex]\(-21k = 9 - 72\)[/tex]
- This simplifies to: [tex]\(-21k = -63\)[/tex]
4. Solve for [tex]\(k\)[/tex]:
- Divide both sides by -21 to solve for [tex]\(k\)[/tex]:
- [tex]\(k = \frac{-63}{-21}\)[/tex]
- Simplify the fraction:
- [tex]\(k = 3\)[/tex]
Therefore, the solution to the equation [tex]\(4(18 - 3k) = 9(k + 1)\)[/tex] is [tex]\(k = 3\)[/tex].
