\( \begin{array}{ll} & \text { Solve for } x: \\ 2.1 & (x-5)(x+3)=0 \\ 2.2 & 2^{x-1}=10-2^{x+1} \\ 2.3 & 5^{3 x-6}=125 \\ 2.4 & \frac{x^{2}-3}{2}=x\end{array} \)

f) \( (-15 a b c+12 a b-9 a c-3 a) \div(-3 a) \)

expunencial \( \left.\left(4^{2}\right)\left(2^{3}\right)^{2 x-5}\right)=8 \)

3.18. Determine el máximo comun divisor de los enteros \( 15,18,24 \) y escríbalo como una combinación lineal de \( 15,18,24 \). 3.19. Sea \( a \in \mathbb{Z}^{+} \)tal que \( \operatorname{mcd}(240, a)=1 \), probar que \( 240 \mid a^{4}-1 \).

42. Julio paid \( 7 \frac{3}{4} \% \) sales tax on an item he bought. He figured that if he had bought the item in a neighboring state where the sales tax is \( 8 \frac{1}{4} \% \), he would have paid \( \$ 75 \) more. What was the cost of the item before tax? (C) \( \$ 15,000.00 \) (IS) \( \$ 3,750.00 \) (C) \( \$ 1,500.00 \) (D) \( \$ 150.00 \) (F) \( \$ 37.50 \)

Find \( n \), \( 3 n-6=18 n^{2} \) A) 0.654 (B) -0.488 (C) 0.654 OR -0.488 (D) No real roots