🧮 algebra

1. **Problem Statement:** We have two rational numbers $a$ and $b$ on a number line, where $a < 0 < b$. The number $c$ is defined as the sum $c = a + b$. We need to determine which

1. **State the problem:** We need to order the expressions $2 - (-10)$, $-2 - 5$, $2 + (-10)$, and $-2 + 5$ from least to greatest. 2. **Recall rules for addition and subtraction o

1. **Stating the problem:** Solve the system of inequalities: $$2x + 3y > 8$$

1. The problem asks to find the "c.d of A.p" for the numbers 3, 4, 9, and 4-8. 2. First, clarify the terms: "A.p" likely means Arithmetic Progression (AP), and "c.d" means common d

1. **State the problem:** Divide the polynomial $4x^2 + 19x + 13$ by the binomial $x + 4$. 2. **Formula and rules:** Polynomial division can be done using long division or syntheti

1. The problem is to find the 8th term of the arithmetic progression (A.P.) with the first three terms given as $-3, -1, 1$. 2. Recall the formula for the $n$th term of an A.P.:

1. **State the problem:** Evaluate the expression $$9.1 + (-3 \frac{4}{5})$$. 2. **Convert the mixed number to an improper fraction:**

1. The problem is to graph the set of values $x$ such that $-1 < x \leq 3$ on a number line. 2. This set describes all numbers greater than $-1$ but less than or equal to $3$.

1. **State the problem:** Diego walks between 9 and 12 miles per week and works out at the gym between 4.5 and 6 hours per week. We need to write a system of inequalities to repres

1. **State the problem:** Find the common difference in the arithmetic sequences (A) 5, 9, 13 and (B) -3, -1, 1. 2. **Formula:** The common difference $d$ in an arithmetic sequence

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

1. The problem is to find the common difference in an arithmetic progression (A.P.). 2. An arithmetic progression is a sequence of numbers where the difference between consecutive

1. **State the problem:** Find the product of the binomials $(x+3)(x+4)$ and verify the sum $x^2 + 3x$. 2. **Formula used:** The product of two binomials $(a+b)(c+d)$ is given by t

1. **State the problem:** We need to find the length of a rectangle given its area and width. 2. **Formula:** The area $A$ of a rectangle is given by the formula:

1. The problem asks to express the area of rectangles formed by tiles as a product of length and as a sum of parts. 2. For part (a), the rectangle has dimensions $(x + 3)$ and $(x^

1. The problem states: A rectangle has an area of 3 square feet and a width of $\frac{1}{2}$ foot. We need to find the length of the rectangle. 2. The formula for the area of a rec

1. Énonçons le problème : Résoudre les équations \( \frac{4x+2}{2x-1} = 0 \) et \( \frac{4}{x-1} - \frac{2}{3-2x} = 0 \). 2. Pour la première équation, une fraction est nulle si et

1. The problem is about drawing graphs of functions, typically in coordinate planes. 2. To draw a function, you need to understand its formula and key features like intercepts, ext

1. The problem is about drawing graphs of functions, typically in coordinate planes. 2. To draw a function graph, you need to understand the function's formula and key features lik

1. **State the problem:** Factor the expression $x^2$. 2. **Recall the factoring rules:**

1. **Problem:** For each pair of functions, identify one characteristic they share and one characteristic that distinguishes them. 2. **Pair a) $f(x) = \frac{1}{x}$ and $g(x) = x$*