2. ( $4 p$ ) a) Find the value of $x$ from the equality:

$$
(x+1)+(x+2)+(x+3)+\cdots+(x+50)=2525
$$

( 3 p ) b) How many natural numbers satisfy the relation:

$$
4 \cdot x+17<100 ?
$$
2. a ) $50 x+(1+2+3+\cdots+50)=2525$

$$
50 x=2525-50 \cdot 51: 2
$$

$$
50 x=2525-1275
$$

$$
x=1250: 50 \Rightarrow x=25
$$

b ) $4 x<100-17 \Rightarrow x<20 \frac{3}{4} \Rightarrow x \in\{0,1,2,3, \ldots, 20\}$

21 natural numbers satisfy the relation