\( 2\frac{1}{4}=\frac{x}{2}+t\leq 1\frac{1}{6} \)

We start with the expression \[ 2\frac{1}{4} = \frac{x}{2} + t \leq 1\frac{1}{6}. \] Step 1. Convert the mixed numbers to improper fractions. - For \(2\frac{1}{4}\): \[ 2\frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{9}{4}. \] - For \(1\frac{1}{6}\): \[ 1\frac{1}{6} = \frac{1 \times 6 + 1}{6} = \frac{7}{6}. \] Step 2. Rewrite the expression with these fractions: \[ \frac{9}{4} = \frac{x}{2} + t \leq \frac{7}{6}. \] Step 3. Analyze the chain. The expression above tells us that \[ \frac{x}{2} + t = \frac{9}{4} \] and at the same time we must have \[ \frac{x}{2} + t \leq \frac{7}{6}. \] But if \(\frac{x}{2} + t = \frac{9}{4}\), then the inequality becomes \[ \frac{9}{4} \leq \frac{7}{6}. \] Step 4. Compare the two fractions. Convert both fractions to decimals or have a common denominator: - \(\frac{9}{4} = 2.25\), - \(\frac{7}{6} \approx 1.1667\). Clearly, \[ 2.25 > 1.1667, \] or equivalently, \[ \frac{9}{4} > \frac{7}{6}. \] Thus, the condition \(\frac{9}{4} \leq \frac{7}{6}\) is false. Step 5. Conclusion. Since the equality forces \(\frac{x}{2} + t\) to equal \(\frac{9}{4}\) and the inequality requires \(\frac{x}{2} + t\) to be less than or equal to \(\frac{7}{6}\), these conditions cannot be simultaneously satisfied. There are no values of \(x\) and \(t\) such that \[ 2\frac{1}{4} = \frac{x}{2} + t \leq 1\frac{1}{6}. \]