Simplify the Expression: x² - 4½x²

To solve this problem, we'll follow these steps:

• Step 1: Identify and label the given terms: $+x^2$ and $+4\frac{1}{2}x^2$.
• Step 2: Determine the coefficients of $x^2$: Here, the first coefficient is $1$ (from $+x^2$) and the second is $4\frac{1}{2}$ (from $+4\frac{1}{2}x^2$).
• Step 3: Convert $4\frac{1}{2}$ to an improper fraction: $4\frac{1}{2} = \frac{9}{2}$.
• Step 4: Subtract the coefficients of the like terms: $1 - \frac{9}{2}$.
• Step 5: Express '1' as a fraction: $1 = \frac{2}{2}$.
• Step 6: Perform the subtraction: $\frac{2}{2} - \frac{9}{2} = -\frac{7}{2}$.
• Step 7: Multiply the resulting coefficient by $x^2$: The simplified term is $-\frac{7}{2}x^2$.
• Step 8: Convert $-\frac{7}{2}$ to a mixed number for clarity: $-\frac{7}{2}$ is equivalent to $-3\frac{1}{2}$.

Therefore, the simplified expression is $-3\frac{1}{2}x^2$.