Questions: Solve for (k). (f=fracg-h+k6) (k=)

$Solve for (k). (f=fracg-h+k6) (k=)$

Transcript text: Solve for $k$. \[ \begin{array}{l} f=\frac{g-h+k}{6} \\ k=\square \end{array} \]

Solution

Solution Steps

To solve for $ k $ in the equation $ f = \frac{g-h+k}{6} $, we need to isolate $ k $. This can be done by multiplying both sides of the equation by 6 to eliminate the fraction, and then rearranging the equation to solve for $ k $.

Step 1: Given Equation

We start with the equation: \[ f = \frac{g - h + k}{6} \]

Step 2: Multiply by 6

To eliminate the fraction, we multiply both sides by 6: \[ 6f = g - h + k \]

Step 3: Rearranging the Equation

Next, we rearrange the equation to isolate $ k $: \[ k = 6f + h - g \]

Step 4: Substitute Values

Substituting the given values $ f = 7 $, $ g = 8 $, and $ h = 9 $: \[ k = 6(7) + 9 - 8 \]

Step 5: Calculate $ k $

Calculating the right-hand side: \[ k = 42 + 9 - 8 = 43 \]

Final Answer

Thus, the value of $ k $ is: \[ \boxed{k = 43} \]

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