🧮 algebra

1. **State the problem:** Simplify and solve the equation $3 (x - 3) - 5 (3 - x) + 12 = 15 - 3 (3 - x)$. 2. **Distribute the terms:** Apply the distributive property to remove pare

1. **State the problem:** We have a table of equivalent ratios with some missing values. The table is: | ? | 14 |

1. **بيان المسألة:** لدينا قطعة أرض مستطيلة الشكل طولها يزيد عن عرضها ب 50 مترًا، ومحيطها 420 مترًا.

1. نبدأ بحل التمرين الأول A: المطلوب هو حساب

1. The problem asks which system of inequalities has no solution set. 2. A system of inequalities has no solution if the inequalities contradict each other, meaning there is no ove

1. **State the problem:** We need to find which pair $(x,y)$ satisfies the system of inequalities: $$x - 2y < 5$$

1. Stating the problem: Simplify the expression $\sqrt{x}5$. 2. Understanding the expression: The expression $\sqrt{x}5$ means $5$ multiplied by the square root of $x$, which can b

1. **State the problem:** We have 2000 people attending the first webinar. 2. **Given data:**

1. **State the problem:** We have the function $g(x) = \frac{1}{11}(6 \cdot 2^x + 7)$ and want to find the greatest constant $k$ such that $g(x) > k$ for all $x$. 2. **Analyze the

1. **State the problem:** A man and his apprentice paint a room. The man takes 1 hour less than the apprentice to paint alone. Together, they take 72 minutes to paint the room. Fin

1. **State the problem:** Solve the equation $5x - 15 = 15$ for $x$. 2. **Write down the equation:**

1. **State the problem:** We need to find the inequality that represents the total money raised from selling tickets before and during the event.

1. **State the problem:** Simplify the expression $$\frac{8r^4 s^9}{4r^3 s^3}$$. 2. **Recall the rules:** When dividing powers with the same base, subtract the exponents: $$\frac{a

1. **State the problem:** Simplify the expression $$\frac{g^7 h^9}{5 g^2 h^7}$$ and express the answer using exponents. 2. **Recall the exponent rules:** When dividing like bases,

1. **State the problem:** Factorise completely the expression $ab^2 - bc$. 2. **Identify common factors:** Look for common factors in both terms. The terms are $ab^2$ and $bc$.

1. **State the problem:** Simplify the expression $$\frac{8 - 4\sqrt{18}}{50}$$. 2. **Simplify the square root:** Note that $$\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{

1. **State the problem:** Simplify the expression $\frac{b^3}{b^0}$. 2. **Recall the exponent rules:** When dividing powers with the same base, subtract the exponents:

1. **State the problem:** Simplify the expression $\left(\frac{1}{4}\right)^{-3}$.\n\n2. **Recall the rule for negative exponents:** For any nonzero number $a$ and integer $n$, $a^

1. **State the problem:** Simplify the expression $$\frac{8 - 4 \sqrt{18}}{50}$$. 2. **Recall the rules:** Simplify the square root first, then simplify the fraction by factoring a

1. Problema: Aplicar la definición de logaritmos para encontrar $x$ en $\log_2 \left( \frac{4\sqrt{2}}{4} \right) = x$. 2. Recordemos que $\log_a b = c$ significa que $a^c = b$.

1. Let's clarify steps 6 and 7 from your problem. 2. Step 6 usually involves simplifying an expression or performing an operation like factoring or canceling terms.