Question

2 1/3 < x + 1 1/3 < 3 1/2​

Answer 1

Ответ:

(1; 2. 1/6)

Пошаговое объяснение:

$2\frac{1}{3}$

(1; 2. 1/6)

Answer 2

To solve the inequality $2 \frac{1}{3} < x + 1 \frac{1}{3} < 3 \frac{1}{2}$, you can follow these steps:

Step 1: Convert Mixed Numbers to Improper Fractions Convert all the mixed numbers to improper fractions for easier calculations.

$2 \frac{1}{3} = \frac{7}{3}$ $1 \frac{1}{3} = \frac{4}{3}$ $3 \frac{1}{2} = \frac{7}{2}$

Step 2: Subtract 1 1/3 from Both Sides Subtract $\frac{4}{3}$ from all parts of the inequality:

$\frac{7}{3} - \frac{4}{3} < x + \frac{4}{3} < \frac{7}{2} - \frac{4}{3}$

Simplify:

$\frac{3}{3} < x + \frac{4}{3} < \frac{10}{2}$

Step 3: Simplify Further $\frac{3}{3} = 1$ and $\frac{10}{2} = 5$, so the inequality becomes:

$1 < x + \frac{4}{3} < 5$

Step 4: Subtract 4/3 from All Parts Subtract $\frac{4}{3}$ from all parts of the inequality:

$1 - \frac{4}{3} < x + \frac{4}{3} - \frac{4}{3} < 5 - \frac{4}{3}$

Simplify:

$-\frac{1}{3} < x < \frac{11}{3}$

So, the solution for the inequality $2 \frac{1}{3} < x + 1 \frac{1}{3} < 3 \frac{1}{2}$ is $-\frac{1}{3} < x < \frac{11}{3}$.