🧮 algebra

1. The problem is to simplify the expression $2x$. 2. This is a simple algebraic expression representing two times the variable $x$.

1. **State the problem:** Multiply the binomials $(a+b)(c+d)$. 2. **Formula used:** Use the distributive property (FOIL method for binomials):

1. **State the problem:** Solve the quadratic equation $$6x^2 - 5x = 0$$. 2. **Formula and rules:** To solve quadratic equations of the form $$ax^2 + bx + c = 0$$, one common metho

1. The problem asks to solve algebraic equations using a consistent method. 2. The general approach is to isolate the variable by performing inverse operations step-by-step.

1. **Stating the problem:** Simplify the expression $$\sqrt[n]{x} \frac{a}{b} \sqrt[n]{x} \binom{n}{k} |x|$$. 2. **Recall the formulas and rules:**

1. **Problem 1: Find the correct formula for $F$ given $C = \frac{5}{9}(F-32)$.** The original formula relates Celsius ($C$) and Fahrenheit ($F$) as:

1. Problem 1: One number is 12 more than another number. Their sum is 48. Find the two numbers. 2. Problem 2: A father is 26 years older than his son. In 4 years, the father will b

1. **State the problem:** Calculate Maru's net pay every payday given a weekly salary of 10000, mandatory contributions of 500, and non-taxable benefits of 1000. 2. **Understand th

1. **Stating the problem:** We are given the sum formula for a series:

1. The problem is to solve the equation $$0 = -\frac{5}{4}(x - \frac{6}{5})$$ for $x$. 2. The equation is in the form $$0 = a(b)$$ where $a = -\frac{5}{4}$ and $b = (x - \frac{6}{5

1. The user request is vague, so let's clarify by showing a simple example of calculations: solving a quadratic equation. 2. Problem: Solve the quadratic equation $$x^2 - 5x + 6 =

1. **State the problem:** We want to find the sum to infinity of the series $$1 - 2x^2 + 3x^3 - 4x^4 + \cdots$$ given that $$|x| < 1$$. 2. **Identify the series type:** This is an

1. **State the problem:** Solve the equation $$-\frac{1}{2} = \frac{3}{2}k + \frac{3}{2}$$ for $k$. 2. **Write down the equation:**

1. **State the problem:** Simplify the expression $3x \times 4 + 2x \times 3 - 4x \times 2 + x + 5$. 2. **Recall the distributive property:** Multiplying a variable by a number mea

1. The problem states the cubic equation $$4x^3 + 3x^2 + 2x = 12$$ and mentions finding its roots. 2. The solution approximates the only real root as $$x \approx 1.136$$ by testing

1. **Problem 1:** (a) Check if set A is a subset of set B.

1. **Problem Statement:** Solve the system of linear equations for each case (b to f) using the matrix method (Gaussian elimination). 2. **Formula and Rules:**

1. **State the problem:** Convert the quadratic function $y = 3x^2 - 12x + 1$ into vertex form and identify the vertex. 2. **Recall the vertex form:** The vertex form of a quadrati

1. **State the problem:** We are given the quadratic function $y = 3x^2 - 12x + 1$ and asked to rewrite it in vertex form and identify the vertex. 2. **Recall the vertex form:** Th

1. Problem b: Solve the system {

1. **State the problem:** We have a rectangle where the length is three times the width, and the perimeter is 96 cm. We need to find the length and width and label the rectangle ac