Question - Solving an Equation with Fractional Coefficients
Solution:
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 $$ k = 2 $$.
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