🧮 algebra

1. **State the problem:** We need to find the slope of the line passing through the points $(-3, -2)$ and $(4, 4)$. 2. **Formula for slope:** The slope $m$ of a line passing throug

1. Planteamos el problema: Encontrar los enteros $m$ tales que $\ln(m+3)$ y $\ln(10-2m)$ estén definidos. 2. Recordemos que el logaritmo natural $\ln(x)$ está definido solo para $x

1. **State the problem:** Find the equation of the line passing through the points $(-6,4)$ and $(-2,2)$ in slope-intercept form $y=mx+b$. 2. **Formula used:** The slope $m$ of a l

1. **Stating the problem:** We are given matrices:

1. **State the problem:** We are given a piecewise function: $$f(x) = \begin{cases} -3 & \text{if } x \leq -2 \\ x - 1 & \text{if } -2 < x \leq 2 \\ 0 & \text{if } x > 2 \end{cases

1. **State the problem:** Solve the equation $12 - 4x = -7x$ for $x$. 2. **Recall the rule:** To solve linear equations, isolate the variable on one side by performing the same ope

1. **State the problem:** We need to find the number of solutions to the equation $$-9 + 7(-2n + 6) = -19 - 14n$$. 2. **Use the distributive property:** Multiply 7 by each term ins

1. **State the problem:** We need to find how many solutions the equation $$12 - 10u = -2 - 10u + 14$$ has. 2. **Simplify both sides:**

1. **State the problem:** Solve the equation $$12 - 20q = 4(-6q - 17)$$ and determine how many solutions it has. 2. **Write the equation:** $$12 - 20q = 4(-6q - 17)$$

1. **State the problem:** Find the number of solutions to the equation $$13g - 3g + 19 = 5 + 10g$$. 2. **Simplify both sides:** Combine like terms on the left side:

1. **State the problem:** Solve the equation $$-16y + y + 20 = -15y + 20$$ and determine how many solutions it has. 2. **Simplify both sides:** Combine like terms on the left side:

1. **State the problem:** Solve the linear equation $-4x + 15 = -9x - 15$ for $x$. 2. **Write down the equation:**

1. **Problem Statement:** We have a square and an equilateral triangle with the same perimeter.

1. **State the problem:** Solve the equation $12 - 4x = -7x$ for $x$. 2. **Recall the rule:** To solve linear equations, isolate the variable on one side by performing inverse oper

1. The vertex of a parabola given by the quadratic function $y = ax^2 + bx + c$ is found using the formula for the $x$-coordinate of the vertex: $$x = -\frac{b}{2a}$$ 2. Once you f

1. **Problem Statement:** A farmer wants to fence a rectangular area with one side along a stream, so only three sides need fencing. The total fence length is 80 m. We need to find

1. **Problem Statement:** Find the x-intercept and y-intercept of the linear function shown in the graph. 2. **Understanding intercepts:**

1. The problem involves understanding the graph of the function shown, which is a line passing through points approximately (-4,-4) and (4,4). 2. The formula for a line is given by

1. **State the problem:** A tank is initially $\frac{5}{9}$ full of water. After pouring in $6 \frac{3}{4}$ jugs of water, the tank becomes $\frac{2}{3}$ full. We need to find the

1. Let's clarify where the term $8x$ comes from in an algebraic expression. 2. Typically, $8x$ represents a term where 8 is the coefficient and $x$ is the variable.

1. **State the problem:** Solve the equation $19x - 5 - 11x = 15 + 3x$ for $x$. 2. **Combine like terms on the left side:**