Questions: Solve the equation below. A -17 -7(k+5)=3k-(8k-1) B 17 C 18 D -18

Transcript text: 5. Solve the equation below. A -17 \[ -7(k+5)=3 k-(8 k-1) \] B 17 C 18 D -18

Solution

Step 1: Distribute and Simplify Both Sides

First, distribute the \(-7\) on the left side of the equation:

\[ -7(k+5) = -7k - 35 \]

The equation now becomes:

\[ -7k - 35 = 3k - (8k - 1) \]

Next, simplify the right side by distributing the negative sign:

\[ 3k - 8k + 1 = -5k + 1 \]

The equation is now:

\[ -7k - 35 = -5k + 1 \]

Step 2: Combine Like Terms

To isolate the variable \(k\), add \(5k\) to both sides:

\[ -7k + 5k - 35 = -5k + 5k + 1 \]

This simplifies to:

\[ -2k - 35 = 1 \]

Step 3: Solve for \(k\)

Add 35 to both sides to isolate the term with \(k\):

\[ -2k - 35 + 35 = 1 + 35 \]

This simplifies to:

\[ -2k = 36 \]

Now, divide both sides by \(-2\) to solve for \(k\):

\[ k = \frac{36}{-2} = -18 \]

The solution to the equation is:

\[ \boxed{k = -18} \]

The answer is D.

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