🧮 algebra

1. **State the problem:** Calculate the value of the expression $$17 + 3 | -5 + (-2) |$$. 2. **Understand the absolute value:** The absolute value of a number is its distance from

1. The problem is to simplify the expression $2 | - 14 + 7 | - (-10)$. 2. Recall that the absolute value $|x|$ is the distance of $x$ from zero on the number line, so it is always

1. **Énoncé du problème :** Factoriser l'expression $ (2x-1)(x+3) + 5(x+3) $.\n\n2. **Formule et règle importante :** Pour factoriser une expression, on cherche un facteur commun d

1. **State the problem:** Solve the linear equation $2x + y = 3$ for $y$ in terms of $x$. 2. **Formula and rules:** To express $y$ as a function of $x$, isolate $y$ on one side of

1. The problem: Understanding what to do when applying the product rule and the bases are not the same. 2. The product rule in algebra for exponents states: $$a^m \times a^n = a^{m

1. Let's start by stating the problem: Understanding the laws of exponents is essential for simplifying expressions involving powers. 2. The main laws of exponents are:

1. **State the problem:** Simplify the expression $2(5)(\frac{3}{2})$. 2. **Recall the multiplication rule:** When multiplying numbers, multiply the numerators and denominators sep

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} x - y = -3 \\ 10x + 4y = 0 \end{cases}$$

1. The problem is to find the mean (average) of the numbers: 61, 45, 52, 48, 53, 49, 57, 46, 60, 54, 58. 2. The formula for the mean of a set of numbers is:

1. **State the problem:** Simplify the expression $2(3x)(\sqrt{2})$. 2. **Recall the rules:** When multiplying constants and variables, multiply the constants together and keep the

1. **State the problem:** Graph the equation $6x - 2y = -14$ by converting it to slope-intercept form. 2. **Recall the slope-intercept form:** The slope-intercept form of a line is

1. **State the problem:** We need to graph the linear equation $x - y = -1$ using its slope and y-intercept. 2. **Rewrite the equation in slope-intercept form:** The slope-intercep

1. The problem is to simplify the expression $\left(\frac{2}{5}\right)$.\n\n2. This expression is already a fraction in simplest form, representing the division of 2 by 5.\n\n3. Th

1. **State the problem:** Solve the equation $$8x - y = 3$$ for $$y$$. 2. **Isolate $$y$$:** To solve for $$y$$, we want to get $$y$$ alone on one side of the equation. Starting wi

1. The problem is to solve the linear equation $$8x + y = 32$$ for $$y$$. 2. To isolate $$y$$, we use the rule of transposition: move $$8x$$ to the other side by subtracting $$8x$$

1. **State the problem:** Solve the equation $y = nx + c$ for $n$. 2. **Recall the formula:** The equation is linear in $n$, and we want to isolate $n$ on one side.

1. **State the problem:** Solve for $n$ in the equation $$K = 9\pi n$$. 2. **Formula and rules:** The equation relates $K$ and $n$ by multiplication with the constant $9\pi$. To is

1. **State the problem:** We need to solve the equation $$P = k + m + n$$ for the variable $$k$$. 2. **Formula and rules:** To isolate $$k$$, we use the rule of inverse operations.

1. **State the problem:** Solve the equation $$5 - 3 = -7$$ for the variable $a$. 2. **Analyze the equation:** The equation given is $$5 - 3 = -7$$, which simplifies the left side

1. **State the problem:** Solve the two-step equation $$2 + 5d = 67$$ for $d$. 2. **Recall the formula and rules:** To solve for $d$, we need to isolate $d$ on one side of the equa

1. The problem asks to find the mean (average) of the numbers 25, 36, 34, 17, 22, 31, and 38. 2. The formula for the mean of a set of numbers is: