Let me solve each question from the uploaded image:

Question 14

"El enunciado: 'Cuando 8 es sustraído de cuatro veces el número x', se expresa por:"

Mathematically, this translates to: $4x - 8$ Answer: d) $4x - 8$

Question 15

"Si a cierto número se le agrega 24, resulta el triple de ese número. ¿Cuál es el número?"

Let the number be $x$. The equation is: $x + 24 = 3x$ Simplify: $24 = 2x \quad \implies \quad x = 12$ Answer: a) $12$

Question 16

"Si al cuadrado de un número se le agregan 9 unidades, resulta el cuadrado del sucesor del número. Entonces el número es:"

Let the number be $x$. The equation is: $x^2 + 9 = (x + 1)^2$ Expand $(x + 1)^2$: $x^2 + 9 = x^2 + 2x + 1$ Simplify: $9 = 2x + 1 \quad \implies \quad 8 = 2x \quad \implies \quad x = 4$ Answer: c) $4$

Question 17

"Si a un número se le agrega 120, resulta 4 veces el exceso del mismo número sobre 60. ¿Cuál es el número?"

Let the number be $x$. The equation is: $x + 120 = 4(x - 60)$ Simplify: $x + 120 = 4x - 240 \quad \implies \quad 120 + 240 = 4x - x \quad \implies \quad 360 = 3x \quad \implies \quad x = 120$ Answer: e) $120$

Question 18

"La diferencia entre los $\frac{5}{6}$ y los $\frac{3}{10}$ de un número es 8. ¿Cuál es el número?"

Let the number be $x$. The equation is: $\frac{5}{6}x - \frac{3}{10}x = 8$ Find a common denominator (LCM of 6 and 10 is 30): $\frac{25}{30}x - \frac{9}{30}x = 8 \quad \implies \quad \frac{16}{30}x = 8$ Simplify: $\frac{8}{15}x = 8 \quad \implies \quad x = 15$ Answer: d) $15$

Would you like a more detailed explanation of any question? Here are some related questions to deepen your understanding:

1. What is the importance of translating word problems into mathematical equations?
2. How do you simplify equations with fractions effectively?
3. Why is it important to verify solutions in mathematical problems?
4. What strategies can be used to solve quadratic equations systematically?
5. How can identifying patterns in problems improve problem-solving efficiency?

Tip: Always double-check your equations, especially when dealing with fractions or exponents, to avoid small errors that might alter the final answer.