🧮 algebra

1. The problem states: When 9 is increased by 3x, the result is greater than 36. We need to find the least possible integer value for $x$. 2. Write the inequality based on the prob

1. **State the problem:** Solve the inequality $12 - 6x > 24$. 2. **Isolate the variable term:** Subtract 12 from both sides:

1. The problem involves understanding the Roman numeral III and the middle V being V prime (V'). 2. Roman numeral III represents the number 3.

1. **State the problem:** Solve the equation $$\log(5x + 6) = 2 \log_{10}(5x + 6)$$ where the base of the first logarithm is not explicitly given, so we assume it is base 10. 2. **

1. The problem asks to solve question 4, but since the exact question is not provided, I will assume it is a typical algebraic problem involving solving an equation or expression.

1. **Stating the problem:** We have a sequence with nth term given by $$T_n = an^3 - 2n^2 + n + d$$ where $a$ and $d$ are constants.

1. **Problem statement:** The first five terms of a sequence are 4, 6, 16, 40, and 81. (i) Determine if the sequence is quadratic or cubic.

1. **State the problem:** Find the domain and range of the piecewise function $$g(x) = \begin{cases} 6x + 7, & x \leq -2 \\ 4 - 3x, & x > -2 \end{cases}$$

1. **State the problem:** Solve the equation $$\frac{3x}{4} - \frac{1}{4}Cx - 20 = \frac{x}{4} + 32$$ where $C$ is a constant. 2. **Rewrite the equation:** Move all terms to one si

1. **State the problem:** We are given a table of distances and fares and need to construct a linear function that models the fare based on distance. 2. **Find the slope $m$:** The

1. **State the problem:** Simplify the expression $$\sqrt{2 + \frac{5}{\sqrt{3}}}$$. 2. **Rewrite the expression:** The expression inside the square root is $$2 + \frac{5}{\sqrt{3}

1. **State the problem:** Simplify the expression $[-3]x 2x$. 2. **Understand the expression:** The expression can be interpreted as multiplication of $-3x$ and $2x$.

1. **State the problem:** Simplify the expression $$\frac{\sqrt{3} \left(3 + \sqrt{\frac{2}{3}}\right) \sqrt{3}}{\sqrt{3}}$$. 2. **Rewrite the expression:** The numerator is $$\sqr

1. **State the problem:** Simplify the expression $4x[-2x]$. 2. **Recall the rule:** Multiplying a number by a product inside brackets means multiplying the number by each term ins

1. The problem is to simplify the surd expression or understand what a surd is. 2. A surd is an irrational root that cannot be simplified to remove the root, such as $\sqrt{2}$ or

1. The problem is to graph a linear function representing the fare (AED) as a function of distance (km). 2. Typically, the fare can be modeled by a linear equation of the form $$y

1. **State the problem:** We are given a fare rule for a taxi fare: $$\text{Fare} = 2 + 0.5d$$ where $d$ is the distance in kilometers. We need to complete the fare table for given

1. نبدأ بطرح التمرين: لنفترض أن لدينا دالة خطية تمثل العلاقة بين المتغيرين $x$ و $y$، ونريد إيجاد معادلة الدالة التي تمر بالنقاط $(1,3)$ و $(4,15)$. 2. نستخدم صيغة ميل المستقيم الت

1. **State the problem:** We are given the quadratic function $$y = 2x^2 - 6x + 4$$ and asked to find the value of $$y$$ when $$x = -2$$. 2. **Substitute the value of $$x$$ into th

1. The problem is to find the value of $\log_{10} 1$. 2. Recall the definition of logarithm: $\log_b a = c$ means $b^c = a$.

1. **State the problem:** Solve for $x$ in the equation $$\log_a(4x) - \log_a(2x+1) = \frac{1}{2} \log_4 4.$$\n\n2. **Recall logarithm properties:**\n- The difference of logarithms