To solve the equation [tex]\(\frac{1}{2} x + 3 = \frac{1}{2} x - 2\)[/tex], let's go through each step carefully.
1. Start with the given equation:
[tex]\[\frac{1}{2} x + 3 = \frac{1}{2} x - 2\][/tex]
2. First, we aim to eliminate the fractional coefficients. Notice that [tex]\(\frac{1}{2} x\)[/tex] appears on both sides of the equation:
[tex]\[\frac{1}{2} x + 3 - \frac{1}{2} x = \frac{1}{2} x - 2 - \frac{1}{2} x\][/tex]
3. Simplify both sides by subtracting [tex]\(\frac{1}{2} x\)[/tex]:
[tex]\[3 = -2\][/tex]
4. Observe the simplified equation [tex]\(3 = -2\)[/tex]. This is a contradiction, meaning there is no value of [tex]\(x\)[/tex] that satisfies the original equation.
Therefore, the equation [tex]\(\frac{1}{2} x + 3 = \frac{1}{2} x - 2\)[/tex] has no solution.
