🧮 algebra

1. The problem is to solve the equation $2x + 3 = 7$ for $x$. 2. We use the basic algebraic principle of isolating the variable $x$ by performing inverse operations.

1. **State the problem:** Find the y-intercept of the equation $4y=12x$. 2. **Rewrite the equation in slope-intercept form:** The slope-intercept form is $y=mx+b$, where $b$ is the

1. **State the problem:** Solve the equation $4y = 12x$ for $y$. 2. **Formula and rules:** To isolate $y$, divide both sides of the equation by 4.

1. The problem is to understand the Singapore MOE method for solving linear systems (LS) clearly. 2. The Singapore MOE method often uses a step-by-step approach to solve linear equ

1. **State the problem:** We need to find how many ice cream sticks Peter, Paul, and Gernard each have given these conditions: - Peter and Paul together have 115 sticks.

1. Énonçons le problème : Trouver la valeur de $f(0,14)$ où $f(x) = \arctan\left(\frac{\sqrt{3} x^3 + \sqrt{3}}{x^3 - 1}\right)$.\n\n2. La fonction $\arctan$ est la fonction arc ta

1. **Problem Statement:** We need to sketch the graphs of the inequalities:

1. **Problem a:** Solve $3(y + 1)^2 - 5 = 43$. 2. **Rewrite the equation:** Add 5 to both sides:

1. **State the problem:** Solve the inequalities:

1. 問題陳述：已知 $a,b$ 皆為正實數，函數 $f(x) = x^3 - 3ax^2 + b$ 的圖形中恰有兩處的一次近似為水平線，且其中一條水平線為 $x$ 軸。請問此函數的對稱中心會在下列哪一個函數圖形上？ 2. 重要公式與規則：

1. The problem is to evaluate the expression $8 \div 2 \times 2 \times 2$. 2. According to the order of operations (PEMDAS/BODMAS), division and multiplication are performed from l

1. The problem is to simplify and solve the equation: $$16x^2 - (4x - 1)(4x + 1) + 2x = 7$$

1. **State the problem:** Solve the system of equations by graphing: $$y = 3x - 2$$

1. **State the problem:** Solve the system of equations by graphing: $$y = (x - 1)^2 + 1$$

1. **State the problem:** Solve the equation $$\frac{g+3}{g-2} = \frac{56}{21}$$ for $g$. 2. **Use the cross-multiplication rule:** For two fractions equal to each other, $$\frac{a

1. **State the problem:** Solve the equation $(x-18)-8=-28$ for $x$. 2. **Write down the equation:**

1. **State the problem:** Simplify the expression $$(-5)^2 - 2 \times (-9) + 6$$ using the correct order of operations. 2. **Recall the order of operations:** Parentheses, Exponent

1. The problem asks: If $f$ is a decreasing function, what can we say about the function $g = f \circ f$ (the composition of $f$ with itself)? 2. Recall that a function $f$ is decr

1. Énonçons le problème : vous souhaitez un calcul mathématique méthodique, par exemple une factorisation. 2. Rappelons la méthode de factorisation : pour factoriser une expression

1. **Problem Statement:** Calculate the sum of each pair of integers given. 2. **Formula and Rules:** Adding integers involves combining positive and negative numbers. Key rules:

1. **State the problem:** We are given the expression $a = 5 + x$ and need to understand or work with it. 2. **Explanation:** This is a simple algebraic expression where $a$ depend