🧮 algebra

1. The problem is to analyze the linear function given by the equation $y=\frac{2}{3}x-2$. 2. This is a linear function of the form $y=mx+b$, where $m$ is the slope and $b$ is the

1. The problem is to analyze the linear function $y = -3x + 2$. 2. This is a linear equation in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept

1. **State the problem:** Find the x-intercept and y-intercept of the line given by the equation $$y=\frac{2}{3}x - 2$$ and graph the line. 2. **Y-intercept:** The y-intercept occu

1. **Stating the problem:** We need to find the region that satisfies the system of inequalities:

1. **State the problem:** Solve the linear equation $4x + 9 = 12$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ on one side of the equation by performing inverse

1. **State the problem:** We need to write a system of equations to find the weight of each large box ($x$) and each small box ($y$) based on the given deliveries. 2. **Define vari

1. **State the problem:** We have two deliveries with large and small boxes. We want to find the weight of each large box ($x$) and each small box ($y$) given the total weights. 2.

1. **State the problem:** Solve the equation $$x - \frac{2x + 1}{x + 1} = \frac{1}{x + 1}$$ for $x$. 2. **Identify the formula and rules:** To solve equations involving fractions,

1. **State the problem:** We have two systems of linear equations and need to determine the nature of their solutions (no solution, unique solution, or infinitely many solutions) a

1. **State the problem:** Solve the equation $$x + \frac{3x + 2}{x + 4} = 2x$$ for $x$. 2. **Identify the formula and rules:** To solve this rational equation, we first eliminate t

1. The problem asks to determine if the given piecewise expression defines a function and to evaluate $f(-3)$, $f(0)$, and $f(6)$.\n\n2. The function is defined as:\n$$f(x) = \begi

1. **State the problem:** Solve the equation $\frac{m}{8h} = -6$ for $m$. 2. **Formula and rules:** To isolate $m$, multiply both sides of the equation by $8h$ to cancel the denomi

1. **State the problem:** Simplify the expression $$\frac{x^2 - 81}{2x^2 + 18x}$$. 2. **Recall formulas and rules:**

1. The problem asks to find the value of $x$ for which the matrix $\begin{bmatrix} 2 & 4 \end{bmatrix}$ is singular. However, this is a 1x2 matrix (a row vector), and singularity i

1. **Problem Statement:** We have a function $V(m)$ representing the volume of water drained from a fish tank after $m$ minutes. Edgar drains 10 gallons each month using a siphon v

1. **Stating the problem:** We are given the efficiency function of two weaving machines combined:

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. We use the basic algebraic principle of isolating the variable $x$ by performing inverse operations.

1. **State the problem:** Simplify the expression $3x + 5x - 2x$. 2. **Recall the rule:** When simplifying algebraic expressions, combine like terms by adding or subtracting their

1. The problem is to evaluate the expression $0.9 \sqrt{0.51}$. 2. Recall that the square root function $\sqrt{x}$ gives the positive number which, when squared, equals $x$.

1. **State the problem:** Simplify the expression $-8 + (-x) - 3 + 7x$. 2. **Identify like terms:** Group the constant terms and the terms with $x$ separately.

1. **State the problem:** Factor the expression $$-8b^2 - 36b$$ completely. 2. **Identify the greatest common factor (GCF):** Both terms have a factor of $$-4b$$ because: