Solve for k. {:[(4k-6)/(3k-9)=(1)/(3)],[k=]:}

Equation setup: Set up the equation based on the given problem. (4k - 6) / (3k - 9) = 1 / 3Cross-multiplication: Cross-multiply to eliminate the fractions. 3 * (4k - 6) = 1 * (3k - 9)Distributing numbers: Distribute the numbers on both sides of the equation. 12k - 18 = 3k - 9Rearranging terms: Move all terms containing k to one side of the equation and constants to the other side. 12k - 3k = -9 + 18Simplifying equation: Simplify both sides of the equation. 9k = 9Dividing by 9: Divide both sides by 9 to solve for k. k = 9 / 9Simplifying fraction: Simplify the fraction to find the value of k. k = 1

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Math Problems

Grade 6

Multiply two decimals: where does the decimal point go?

Full solution

Q. Solve for

k

\newline

\begin{array}{l} \frac{4 k-6}{3 k-9}=\frac{1}{3} \\ k= \end{array}

Equation setup: Set up the equation based on the given problem. $\newline$ $(4k - 6) / (3k - 9) = 1 / 3$
Cross-multiplication: Cross-multiply to eliminate the fractions. $3 \times (4k - 6) = 1 \times (3k - 9)$
Distributing numbers: Distribute the numbers on both sides of the equation. $12k - 18 = 3k - 9$
Rearranging terms: Move all terms containing $k$ to one side of the equation and constants to the other side. $12k - 3k = -9 + 18$
Simplifying equation: Simplify both sides of the equation. $9k = 9$
Dividing by $9$ : Divide both sides by $9$ to solve for $k$ . $k = \frac{9}{9}$
Simplifying fraction: Simplify the fraction to find the value of $k$ . $k = 1$