USING EQUATIONS to solve WORD PROBLEMS Directions: Set up and solve an equation for each problem below. 1. The product of 7 and a number, increased by 3, is equal to twice the number, subtracted from 39. Find the number.

Divide 15 into two parts such that the sum of their reciprocals is \( \frac{3}{10} \).

Find the two natural numbers which differ by 5 and the sum of whose squares is 97.

Hallar los autovalores reales \( y \) autovectores de \( \mathbb{R}^{n}, y \) una base de au- tovectores cuando sea posible, de las matrices: a) \( \left(\begin{array}{rr}4 & 6 \\ -3 & -5\end{array}\right) \), b) \( \left(\begin{array}{rr}5 & -1 \\ -1 & 1\end{array}\right) \), c) \( \left.\left(\begin{array}{cc}1 & -2 \\ -2 & 3\end{array}\right), d\right)\left(\begin{array}{rrr}2 & 2 & -1 \\ 0 & -2 & 0 \\ -1 & 0 & 0\end{array}\right) \)

factoring, that \( A(x)=(x-2)(-x+1) \)

d) \( \begin{aligned} & f(x)=\left\{\begin{array}{c}3 x+4,-1 \leq x<2 \\ 1+x, 2 \leq x \leq 5\end{array}\right. \\ & \operatorname{Dom}(f)=\{x:-1 \leq x<5\}=[-1,5)\end{aligned} \)