https://file.aiquickdraw.com/mathbot/file/1726193785994ech0p6pn.jpg

The equation in the image is:

\[
\frac{1}{2}(10k - 16) + 11 = -2
\]

Let's solve this step by step.

### Step 1: Distribute \(\frac{1}{2}\)
Distribute \(\frac{1}{2}\) to both terms inside the parentheses:

\[
\frac{1}{2}(10k) - \frac{1}{2}(16) = 5k - 8
\]

Now the equation becomes:

\[
5k - 8 + 11 = -2
\]

### Step 2: Combine like terms
Combine \(-8\) and \(11\):

\[
5k + 3 = -2
\]

### Step 3: Isolate the variable \(k\)
Subtract 3 from both sides:

\[
5k = -2 - 3
\]
\[
5k = -5
\]

### Step 4: Solve for \(k\)
Divide both sides by 5:

\[
k = \frac{-5}{5} = -1
\]

So, the solution is:

\[
k = -1
\]

Would you like further details or have any questions about this?

### Related questions:
1. How can I check if my solution for \(k\) is correct?
2. What happens if the equation had a different fraction instead of \(\frac{1}{2}\)?
3. Can this type of

Solve the equation: 1/2(10k - 16) + 11 = -2

Learn how to solve the linear equation 1/2(10k - 16) + 11 = -2. This problem demonstrates key algebraic techniques such as distributing fractions and isolating variables. Suitable for students in Grades 7-9.

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