🧮 algebra

1. **State the problem:** Solve the inequality $$3x - 5 > 7$$ and determine which of the given options is correct. 2. **Recall the rule for inequalities:** When solving inequalitie

1. **Stating the problem:** We need to find which inequality matches the number line shown. 2. **Analyzing the number line:** The number line has a solid circle at 2 and shading ex

1. The problem asks to identify the inequality that describes "The value is more than or equal to 12." 2. The phrase "more than or equal to" means the value can be greater than 12

1. **State the problem:** We need to find the rule for the function $i(x)$ given a table of bounded linear functions with some known properties for $f(x)$, $g(x)$, $h(x)$, and unkn

1. **State the problem:** Simplify and verify the equation $$\frac{5}{x+3} + \frac{2}{x-3} = \frac{5}{x^2 - 9}$$ where the denominators are expressions involving $x$. 2. **Recall t

1. **State the problem:** Solve the equation $$\frac{2}{3} + \frac{1}{y} = \frac{1}{5}$$ for $y$. 2. **Isolate the term with $y$:** Subtract $\frac{2}{3}$ from both sides:

1. **State the problem:** Solve the equation $$\frac{2}{3} + \frac{1}{y} = \frac{1}{5}$$ for $y$. 2. **Isolate the term with $y$:** Subtract $\frac{2}{3}$ from both sides:

1. **Problem 19:** Solve the equation $$\sqrt{y - 5} + 5 = y$$ 2. **Step 1:** Isolate the square root term:

1. **Énoncé du problème :** Simplifier les expressions suivantes impliquant des exponentielles et des logarithmes naturels. 2. **Rappel de la formule importante :** Pour tout $x >

1. **State the problem:** Solve the inequality $\ln(x) > 4$. 2. **Recall the definition and properties:** The natural logarithm function $\ln(x)$ is defined for $x > 0$ and is the

1. **Stating the problems:** We need to solve the following equations:

1. **State the problem:** Solve the inequality $|x-2| > 2|x-1|$. 2. **Recall the definition of absolute value:** For any real number $a$, $|a| = a$ if $a \geq 0$, and $|a| = -a$ if

1. **State the problem:** We need to simplify the expression $$(3 - \sqrt{2})(4 + \sqrt{2})$$. 2. **Formula used:** To multiply two binomials, use the distributive property (FOIL m

1. **Stating the problem:** We are given the system of equations:

1. **State the problem:** Solve the system of linear equations: $$\begin{cases}x-2y=4\\ 3x+y=9\end{cases}$$

1. **Problem Statement:** We are given a line on a Cartesian plane that crosses the y-axis near $y=6$ and the x-axis near $x=4$. We need to find the slope of this line in simplest

1. **State the problem:** Solve the linear equation $x - 2y = -4$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation. This

1. **Problem Statement:** Solve the system of equations derived from the equation $x^2 + y^2 + z^2 = 14$ using the Gaussian elimination method. 2. **Important Note:** Gaussian elim

1. The problem is to find the turning point (vertex) of the parabola given by the equation $y=(x+a)^2 + b$. 2. The general form of a parabola's vertex form is $y=(x-h)^2 + k$, wher

1. **Problem Statement:** Solve the system of quadratic equations: $$\begin{cases} x^2 + y^2 + z^2 = 14 \\ x^2 - y^2 + 2z^2 = 15 \\ x^2 + 2y^2 + 3z^2 = 36 \end{cases}$$

1. **State the problem:** We need to compare the rates of change (slopes) of the data given in the table and the graph. 2. **Rate of change formula:** The rate of change between tw