Answer :
To solve the equation [tex]\(4(18 - 3k) = 9(k + 1)\)[/tex], we need to follow these steps:
1. Distribute the 4 on the left side:
[tex]\[ 4(18 - 3k) = 4 \cdot 18 - 4 \cdot 3k = 72 - 12k \][/tex]
2. Distribute the 9 on the right side:
[tex]\[ 9(k + 1) = 9 \cdot k + 9 \cdot 1 = 9k + 9 \][/tex]
3. Set the two expressions equal to each other:
[tex]\[ 72 - 12k = 9k + 9 \][/tex]
4. Combine like terms by moving all the [tex]\(k\)[/tex]-terms to one side and constants to the other:
[tex]\[ 72 - 12k = 9k + 9 \][/tex]
Subtract [tex]\(9k\)[/tex] from both sides:
[tex]\[ 72 - 12k - 9k = 9 \][/tex]
This simplifies to:
[tex]\[ 72 - 21k = 9 \][/tex]
5. Isolate the [tex]\(k\)[/tex]-term by subtracting 72 from both sides:
[tex]\[ -21k = 9 - 72 \][/tex]
Simplify the constant on the right side:
[tex]\[ -21k = -63 \][/tex]
6. Solve for [tex]\(k\)[/tex] by dividing both sides by [tex]\(-21\)[/tex]:
[tex]\[ k = \frac{-63}{-21} \][/tex]
Simplify the fraction:
[tex]\[ k = 3 \][/tex]
Thus, the solution to the equation [tex]\(4(18 - 3k) = 9(k + 1)\)[/tex] is:
[tex]\[ k = 3 \][/tex]
1. Distribute the 4 on the left side:
[tex]\[ 4(18 - 3k) = 4 \cdot 18 - 4 \cdot 3k = 72 - 12k \][/tex]
2. Distribute the 9 on the right side:
[tex]\[ 9(k + 1) = 9 \cdot k + 9 \cdot 1 = 9k + 9 \][/tex]
3. Set the two expressions equal to each other:
[tex]\[ 72 - 12k = 9k + 9 \][/tex]
4. Combine like terms by moving all the [tex]\(k\)[/tex]-terms to one side and constants to the other:
[tex]\[ 72 - 12k = 9k + 9 \][/tex]
Subtract [tex]\(9k\)[/tex] from both sides:
[tex]\[ 72 - 12k - 9k = 9 \][/tex]
This simplifies to:
[tex]\[ 72 - 21k = 9 \][/tex]
5. Isolate the [tex]\(k\)[/tex]-term by subtracting 72 from both sides:
[tex]\[ -21k = 9 - 72 \][/tex]
Simplify the constant on the right side:
[tex]\[ -21k = -63 \][/tex]
6. Solve for [tex]\(k\)[/tex] by dividing both sides by [tex]\(-21\)[/tex]:
[tex]\[ k = \frac{-63}{-21} \][/tex]
Simplify the fraction:
[tex]\[ k = 3 \][/tex]
Thus, the solution to the equation [tex]\(4(18 - 3k) = 9(k + 1)\)[/tex] is:
[tex]\[ k = 3 \][/tex]