Solving an Equation with Fractional Coefficients
The equation given in the image is \( 3 + \frac{3}{2}k = 4k - 2 \). To solve for \( k \), follow these steps:
1. First, try to get all the terms with \( k \) on one side of the equation and the constant terms on the other side.
2. Subtract \( \frac{3}{2}k \) from both sides to move the \( k \) terms to the right side:
\( 3 = 4k - \frac{3}{2}k - 2 \)
3. Combine like terms on the right side. To combine \( 4k \) and \( -\frac{3}{2}k \), you can convert \( 4k \) to \( \frac{8}{2}k \) to have a common denominator:
\( 3 = \left( \frac{8}{2}k - \frac{3}{2}k \right) - 2 \)
4. Now, subtract the coefficients:
\( 3 = \frac{5}{2}k - 2 \)
5. Next, add 2 to both sides to move the constant terms to the left side:
\( 3 + 2 = \frac{5}{2}k \)
6. Combine the constants:
\( 5 = \frac{5}{2}k \)
7. Now, to solve for \( k \), multiply both sides of the equation by the reciprocal of \( \frac{5}{2} \), which is \( \frac{2}{5} \):
\( 5 \times \frac{2}{5} = \frac{5}{2}k \times \frac{2}{5} \)
8. This simplifies nicely, as the \( \frac{5}{2} \) and \( \frac{2}{5} \) cancel each other on the right side:
\( k = 5 \times \frac{2}{5} \)
9. After cancellation, we get:
\( k = 2 \)
So, the solution to the equation is \( k = 2 \).
