🧮 algebra

1. **Problem Statement:** We are given three expressions to expand:

1. **Énoncé du problème** : Résoudre l'équation quadratique $$X^2 - 3X + 2 = 0$$. 2. **Formule du discriminant** : Pour une équation quadratique $$ax^2 + bx + c = 0$$, le discrimin

1. **State the problem:** We are given a table of values for $x$ and $y$: $$\begin{array}{c|cccc}

1. **Problem Statement:** We are given a table of values for $x$ and $y$:\\ \begin{array}{c|cccc}

1. **State the problem:** Find the slope of line $n$ passing through points $A(5,6)$ and $B(15,12)$. 2. **Formula for slope:** The slope $m$ of a line through points $(x_1,y_1)$ an

1. **State the problem:** Find the slope of the line passing through points $A(-1,6)$ and $B(5,4)$. 2. **Recall the slope formula:**

1. **State the problem:** We need to graph the linear inequality $$y < \frac{1}{4}x + 1$$ on a coordinate grid with x- and y-axes ranging from -5 to 5. 2. **Understand the inequali

1. **State the problem:** We want to find the initial amount of water in the tub, which means the amount of water at time $x = 0$ minutes. 2. **Given equation:** The amount of wate

1. **State the problem:** Solve the inequality $$6x - 1 > 11$$ for $x$. 2. **Add 1 to both sides** to isolate the term with $x$:

1. **State the problem:** Solve the inequality $$9x + 9 \leq 27$$ for $x$. 2. **Isolate the term with $x$:** Subtract $9$ from both sides to get $$9x + 9 - 9 \leq 27 - 9$$ which si

1. The problem states: "It was $x$ $z$ $w$ or $y$." 2. Since this is a statement involving variables $x$, $z$, $w$, and $y$, but no explicit question or equation is given, there is

1. The problem asks to find the interval, the starting point, and the 5 x-values. 2. To solve this, we need to understand what interval means and how to determine x-values starting

1. **State the problem:** We want to determine if $\sqrt{5} < \sqrt{5}^{\sqrt{5}}$ is true. 2. **Rewrite the inequality:** The inequality is $\sqrt{5} < \left(\sqrt{5}\right)^{\sqr

1. **State the problem:** We are given four numbers $0.5$, $4$, $1.6$, and $0.2$ and asked to write proportions using these numbers and perform all possible switches and changes. 2

1. **Problem:** Solve each linear system using **elimination**. 2. **a) Solve the system**

1. **Problem Statement:** Solve each linear system using the method of elimination. ---

1. **State the problem:** Divide the polynomial $$x^3 + 2x^2 - 8x + 5$$ by the binomial $$x - 1$$ using long division. 2. **Recall the formula:** When dividing polynomials, the div

1. **State the problem:** Solve the inequality $$\frac{x}{x - 6} > 0$$ and express the solution set in interval notation. 2. **Rewrite the inequality:** Move all terms to the left

1. **State the problem:** Solve the inequality $$\frac{2 - 2x}{5x + 3} \leq 0$$ and express the solution set in interval notation. 2. **Rewrite the inequality:** Define $$f(x) = \f

1. **State the problem:** Solve the inequality $$\frac{-x + 5}{x - 7} \geq 0$$ and express the solution set in interval notation. 2. **Identify critical points:** The numerator is

1. **Problem a:** Solve the system \(\begin{cases} y = -6x \\ y = -2x + 8 \end{cases}\) using substitution. 2. Since both expressions equal \(y\), set them equal: \(-6x = -2x + 8\)