🧮 algebra

1. **Stating the problem:** Solve the inequality $5x + 3y > -15$ for $y$ in terms of $x$. 2. **Formula and rules:** To isolate $y$, we use basic algebraic operations: addition, sub

1. The problem is to find a function $f(x)$ such that $f(0)=7$, $f(1)=4$, and $f(2)=3$. 2. We can try to find a polynomial function that fits these points. Since we have three poin

1. **Stating the problem:** We have a scatter plot with points (1,7), (2,4), and (3,2) representing input-output pairs (Entrée, Sortie). We want to find the table of values and an

1. **Problem statement:** Find the number of pairs of natural numbers $(x,y)$ such that $$7x + 13y \leq 1000.$$ 2. **Understanding the problem:** We want to count all pairs $(x,y)$

1. **State the problem:** Solve the system of linear equations: $$3x - 2y = 7$$

1. **Problem Statement:** Find the Highest Common Factor (HCF) and Least Common Multiple (LCM) of the numbers 378, 180, and 420. 2. **Formula and Rules:**

1. **Stating the problem:** Find the Highest Common Factor (HCF) and Least Common Multiple (LCM) of the numbers 12, 21, and 15. 2. **Formula and rules:**

1. **Problem Statement:** Given that $p$ and $q$ are natural numbers and $p$ is a multiple of $q$, find the Highest Common Factor (HCF) of $p$ and $q$. 2. **Understanding the probl

1. **Problem Statement:** Given two positive integers $p$ and $q$ expressed as $p = a b^2$ and $q = a^3 b$, where $a$ and $b$ are prime numbers, find the least common multiple (LCM

1. **State the problem:** Factorize the cubic polynomial $$3x^3 + 26x^2 + 61x + 30$$. 2. **Recall the method:** To factor a cubic polynomial, we try to find rational roots using th

1. **State the problem:** We need to find the length and width of a rectangle where the area is 55 yd² and the length is 4 yd less than three times the width. 2. **Write the formul

1. **Stating the problem:** We want to find the value of $a$ such that the expression $M = 2^3 \times 3^2 \times a$ is a perfect cube. 2. **Recall the rule for perfect cubes:** A n

1. **State the problem:** Solve the equation $$\log_3(3x^2) + \log_3(3) = 2$$ for $x$. 2. **Recall the logarithm property:** The sum of logarithms with the same base can be combine

1. **State the problem:** Solve the logarithmic equation $$\log_2 x + \log_2 (x - 2) = 3$$ for $x$. 2. **Recall the logarithm property:** The sum of logarithms with the same base c

1. **State the problem:** Solve the equation $$\log_2(x^2 - x - 6) = 2$$ and find the exact solutions and their approximations to the nearest tenth. 2. **Recall the logarithm defin

1. **State the problem:** We need to sketch the graph of the function $$f(x) = 3x^4 - 4x^3$$. 2. **Understand the function:** This is a polynomial function of degree 4. The general

1. **Problem statement:** We need to find three consecutive odd numbers whose sum is 69, and then identify the third number in the sequence. 2. **Define variables:** Let the first

1. **State the problem:** We need to find the sixth number in a sequence of 6 consecutive integers whose sum is 387. 2. **Set up variables:** Let the first integer be $x$. Then the

1. **State the problem:** We need to find the first of 4 consecutive even numbers whose sum is 36. 2. **Define variables:** Let the first even number be $x$. Then the next three co

1. **Problem statement:** We are given that the sum of 6 consecutive odd numbers is 204, and we need to find the fourth number in this sequence. 2. **Define variables:** Let the fi

1. **State the problem:** We have two numbers, one is positive and is 3 times the other. If we add 2 to the larger number and 5 to the smaller number, then one becomes twice the ot