Questions: Solve the equation 1/2(k-5)=3/4. k=

Solution Steps

The given equation is:

\[ \frac{1}{2}(k-5) = \frac{3}{4} \]

First, distribute the \(\frac{1}{2}\) across the terms inside the parentheses:

\[ \frac{1}{2} \cdot k - \frac{1}{2} \cdot 5 = \frac{3}{4} \]

This simplifies to:

\[ \frac{1}{2}k - \frac{5}{2} = \frac{3}{4} \]

To eliminate the fractions, multiply every term by the least common denominator (LCD) of the fractions, which is 4:

\[ 4 \left(\frac{1}{2}k\right) - 4 \left(\frac{5}{2}\right) = 4 \left(\frac{3}{4}\right) \]

This simplifies to:

\[ 2k - 10 = 3 \]

Add 10 to both sides of the equation to isolate the term with \(k\):

\[ 2k - 10 + 10 = 3 + 10 \]

\[ 2k = 13 \]

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

\[ k = \frac{13}{2} \]

Final Answer