🧮 algebra

1. The problem asks to convert interval notation solutions of an absolute value inequality into set-builder notation. 2. Recall that interval notation like $(-\infty, -34) \cup [10

1. **State the problem:** Solve the equation $$6a + 12 = 2(3a - 8)$$ for the variable $a$. 2. **Write the formula and rules:** To solve equations with variables on both sides, firs

1. The problem asks to express the solutions of the inequality $$-34 < x < 10$$ in three different ways and identify the correct interval notation. 2. This inequality means that $x

1. **State the problem:** We have an arched bridge 30 m wide and 40 m tall at the highest point. We want to check if a sailboat with a 25 m tall sail can fit under the bridge 6 m a

1. **State the problem:** Simplify the expression $$\left(\frac{5}{2}+\frac{1}{4}-\frac{7}{8}\right) : \left(-\frac{3}{16}\right) - \frac{5}{3} \left(-\frac{2}{7}\right) + \left(-\

1. **State the problem:** Simplify and analyze the expression $a^2 - ab + 2b - 4$ and the expression $a^2 + 2a + 2b - b^2$. 2. **First expression:** $a^2 - ab + 2b - 4$

1. Planteamos el problema: Factorizar la expresión $45 r^3 s + 20 r s^3$ usando el Factor Común Mayor (FCM). 2. Identificamos los factores comunes en cada término:

1. **State the problem:** Solve the equation $3a - 7 = 26$ for $a$. 2. **Add 7 to both sides:**

1. **State the problem:** Solve the equation $ (3x - 4)(2x - 13) = 0 $. 2. **Formula and rule:** The zero product property states that if $ab = 0$, then either $a = 0$ or $b = 0$.

1. **State the problem:** You have 25 coins total, all nickels and quarters, with a total value of 3.85. Find the number of nickels $n$ and quarters $q$.

1. **State the problem:** Simplify the expression $xy^2 + yx^2$. 2. **Identify common factors:** Notice that both terms contain the factors $x$ and $y$.

1. **State the problem:** Simplify the expression $4X + 5X$. 2. **Formula and rules:** When adding like terms, add their coefficients and keep the variable the same.

1. **State the problem:** Solve the equation $$4(x - 5) = 25$$ for $$x$$ using two strategies. 2. **Strategy A: Use the Distributive Property**

1. **State the problem:** Solve the equation $$300 - 2y + 270 - \frac{3x}{2} = 300$$ for the variables involved. 2. **Combine like terms:** Add the constants on the left side:

1. **بيان المسألة:** لدينا متتالية عددية $U_n$ معرفة على مجموعة الأعداد الطبيعية، ونريد إثبات بعض الخصائص المتعلقة بها. 2. **التمرين الأول:** تحقق أن $24 + 42 + 10$، ماذا تستنتج؟

1. Problem: Nađi $m$ i $k$ u linearnoj funkciji $y = (3m + 2)x + 2k - m$ tako da je graf funkcije paralelan sa pravom $2x - y - 8 = 0$ i da je površina trougla koji graf pravi sa k

1. نبدأ ببيان المسألة: لدينا متتالية عددية $U_n$ معرفة على مجموعة الأعداد الطبيعية، ونريد إثبات بعض الخصائص المتعلقة بها. 2. المعطى الأول: تحقق أن $24 + 42 + 10$، ونريد استنتاج شيء

1. Problem: Izračunajte drugu derivaciju funkcije $$f(x) = \sinh\left(\frac{1}{x^2 - 4}\right)$$. 2. Formula: Koristimo lančanu i pravilo za derivaciju hiperboličkog sinusa:

1. **State the problem:** Find the quotient of $6.208 \times 10^9$ and $9.7 \times 10^4$ expressed in scientific notation. 2. **Recall the formula for division of numbers in scient

1. **State the problem:** We are given the function $y=\pi^{2t}$ and want to understand its form and behavior. 2. **Formula and explanation:** The function is an exponential functi

1. **State the problem:** Calculate the value of $A$ given by the formula $A = 8000 e^{0.06 \times 8}$. 2. **Formula and explanation:** This is an exponential growth formula where