4) Write an expression that is equi 4egroup the like terms. \( \begin{aligned} \frac{1}{4} x+1+\frac{3}{4} x-\frac{2}{3}-\frac{1}{2} x & =\frac{1}{4} \\ & =\end{aligned} \)

Certainly! Let's simplify the given expression by grouping like terms. **Original Expression:** \[ \frac{1}{4}x + 1 + \frac{3}{4}x - \frac{2}{3} - \frac{1}{2}x \] **Step 1: Group Like Terms** - **Combine the \(x\)-terms:** \[ \frac{1}{4}x + \frac{3}{4}x - \frac{1}{2}x \] - **Combine the constant terms:** \[ 1 - \frac{2}{3} \] **Step 2: Simplify Each Group** - **Simplify the \(x\)-terms:** \[ \frac{1}{4}x + \frac{3}{4}x = \left(\frac{1}{4} + \frac{3}{4}\right)x = 1x \] \[ 1x - \frac{1}{2}x = \frac{1}{2}x \] - **Simplify the constant terms:** \[ 1 - \frac{2}{3} = \frac{3}{3} - \frac{2}{3} = \frac{1}{3} \] **Step 3: Combine the Simplified Groups** \[ \frac{1}{2}x + \frac{1}{3} \] **Final Simplified Expression:** \[ \frac{1}{2}x + \frac{1}{3} \] This expression is equivalent to the original one, with like terms grouped and simplified.