🧮 algebra

1. **State the problem:** We need to find the slope of the line passing through the points $(-8, -10)$ and $(8, 8)$. The slope represents the "rise" over the "run" between these tw

1. **State the problem:** Expand the expression $x + x^2$. 2. **Recall the expansion rule:** When expanding, we distribute terms if there are parentheses or combine like terms if p

1. **State the problem:** Solve the equation $$\frac{1}{1 - \sqrt{x}} = 1 - \frac{\sqrt{x}}{\sqrt{x} - 1}$$ for $x$. 2. **Rewrite the equation:** Notice that $\sqrt{x} - 1 = -(1 -

1. **State the problem:** Solve the inequality $$-x^2 + 6x \leq 5$$ and graph the solution on the number line. 2. **Rewrite the inequality:** Move all terms to one side to set the

1. **State the problem:** Solve the inequality $$x^2 - 10x > -24$$ and graph the solution on the number line. 2. **Rewrite the inequality:** Move all terms to one side to set the i

1. **State the problem:** We need to write an expression for the total cost of a basketball jersey that costs 8 dollars plus 1 dollar for each letter printed on it.

1. **Problem statement:** Find the difference between Neptune's and Mercury's distances from the sun. 2. **Given data:**

1. **State the problem:** We want to find which function is equivalent to $f(x) = (x + 3)(x - 9)$ and matches the given handwritten expression $x^2 - 6x - 27$. 2. **Expand the orig

1. **State the problem:** Solve the equation $$\frac{2x+4}{3} = 5$$ for $x$. 2. **Formula and rules:** To solve for $x$, multiply both sides of the equation by the denominator to e

1. **State the problem:** We are given a V-shaped absolute value graph with vertex at $(-4, 2)$ opening upwards. We need to find the equation of the function in the form $a|x - h|

1. **State the problem:** We are given a V-shaped graph centered at the origin (0,0) and extending upwards symmetrically along the y-axis. We need to write the function $g(x)$ in t

1. **State the problem:** We need to find the value of $x$ using ratios. 2. **Understand ratios:** A ratio compares two quantities and can be written as $\frac{a}{b} = \frac{c}{d}$

1. The problem is to write the absolute value function $g(x)$ in the form $a|x - h| + k$ given the vertex and the shape of the graph. 2. The vertex of the graph is given as $(-6, 2

1. The problem is to write the equation of the given V-shaped graph in the form $a|x - h| + k$, where $a$, $h$, and $k$ are integers or simplified fractions. 2. The graph is a stan

1. **State the problem:** Find the slope and y-intercept of the line given by the equation $$y = - \frac{3}{2}x - \frac{5}{2}$$. 2. **Recall the slope-intercept form:** The equatio

1. **State the problem:** We need to write the function $g(x)$ in the form $a|x - h| + k$, where $a$, $h$, and $k$ are integers or simplified fractions. 2. **Analyze the graph:** T

1. **State the problem:** Find the slope and y-intercept of the line given by the equation $$y = 2 - 4x$$. 2. **Rewrite the equation in slope-intercept form:** The slope-intercept

1. **State the problem:** Solve the system of linear equations: $$y = -3x - 5$$

1. The problem is to find the point of intersection $(x,y)$ of the two lines given by the equations: $$y = -3x - 5$$

1. **Problem Statement:** Classify the system of linear equations and find the solution if it exists. ---

1. **State the problem:** We are given three systems of linear equations (System A, B, and C). We need to classify each system as "consistent dependent," "consistent independent,"