B2. The expression is $2-\frac{x-2}{5}+\frac{1+x}{4}$.

A. Calculate the value of the expression for $x=5$.

B. Determine the value of $x$ such that the value of the expression is 4.

C. Determine the value of $x$ such that the value of the expression is at least 2.

D. Find the smallest natural number $x$ such that the value of the expression is an integer.
B2. For $x=5$, the value of the expression $2-\frac{x-2}{5}+\frac{1+x}{4}=2-\frac{5-2}{5}+\frac{1+5}{4}=\frac{29}{10}$.

We write the equation $2-\frac{x-2}{5}+\frac{1+x}{4}=4$. The solution to the equation is $x=27$.

We write the inequality $2-\frac{x-2}{5}+\frac{1+x}{4} \geq 2$. The solution to the inequality is $x \geq-13$.

We simplify the expression $2-\frac{x-2}{5}+\frac{1+x}{4}=\frac{x+53}{20}$. The smallest natural number $x$ for which the value of the expression is an integer is $x=7$.

![](https://cdn.mathpix.com/cropped/2024_06_07_bbf95781e2fd378a6604g-07.jpg?height=66&width=1556&top_left_y=1326&top_left_x=296)

![](https://cdn.mathpix.com/cropped/2024_06_07_bbf95781e2fd378a6604g-07.jpg?height=60&width=1542&top_left_y=1398&top_left_x=311)

![](https://cdn.mathpix.com/cropped/2024_06_07_bbf95781e2fd378a6604g-07.jpg?height=48&width=1488&top_left_y=1455&top_left_x=364)

![](https://cdn.mathpix.com/cropped/2024_06_07_bbf95781e2fd378a6604g-07.jpg?height=60&width=1542&top_left_y=1515&top_left_x=311)

![](https://cdn.mathpix.com/cropped/2024_06_07_bbf95781e2fd378a6604g-07.jpg?height=51&width=1488&top_left_y=1571&top_left_x=364)

D. The calculated smallest natural number $x$ for which the value of the expression is an integer: $x=7$. 1 t