Identify equation and ask: Identify the equation given and what is being asked. The equation given is 4/9k = 8, and we are asked to find the value of k.Isolate variable by multiplying: Isolate the variable k by multiplying both sides of the equation by the reciprocal of the coefficient of k. The coefficient of k is 4/9, so the reciprocal is 9/4. Multiply both sides of the equation by 9/4 to isolate k. (9/4) * (4/9k) = (9/4) * 8Perform multiplication on both sides: Perform the multiplication on both sides of the equation. On the left side, (9/4) * (4/9) simplifies to 1, leaving us with k. On the right side, (9/4) * 8 simplifies to 18. So, k = 18.

Grade 7

Solve equations involving like terms

Full solution

\frac{4}{9}k = 8

Identify equation and ask: Identify the equation given and what is being asked. $\newline$ The equation given is $\frac{4}{9}k = 8$ , and we are asked to find the value of $k$ .
Isolate variable by multiplying: Isolate the variable $k$ by multiplying both sides of the equation by the reciprocal of the coefficient of $k$ . The coefficient of $k$ is $\frac{4}{9}$ , so the reciprocal is $\frac{9}{4}$ . Multiply both sides of the equation by $\frac{9}{4}$ to isolate $k$ . \left(\frac{$9$}{$4$}\right) \times \left(\frac{$4$}{$9$}k\right) = \left(\frac{$9$}{$4$}\right) \times \(8
Perform multiplication on both sides: Perform the multiplication on both sides of the equation. $\newline$ On the left side, $(\frac{9}{4}) \times (\frac{4}{9})$ simplifies to $1$ , leaving us with $k$ . $\newline$ On the right side, $(\frac{9}{4}) \times 8$ simplifies to $18$ . $\newline$ So, $k = 18$ .