🧮 algebra

1. We are asked to solve the inequality $$|x^2 - 2x - 3| < 3$$. 2. Recall that for any expression $A$, the inequality $|A| < b$ (where $b > 0$) means $$-b < A < b$$.

1. The problem is to find the value of $\sqrt{8704}$. 2. The square root of a number $x$ is a value $y$ such that $y^2 = x$.

1. **State the problem:** Simplify the expression $15x^2y - 10xy^3$. 2. **Identify common factors:** Both terms have common factors of $5xy$.

1. **State the problem:** Find the x- and y-intercepts of the equation $$y = 15x - 3$$. 2. **Recall the definitions:**

1. **State the problem:** Find the greatest common factor (GCF) of the polynomial expression $15x^2y - 10xy^3$. 2. **Recall the formula and rules:** The GCF of terms is the product

1. The problem involves understanding set notation for domain and range of functions or relations. 2. The domain is the set of all possible input values (x-values), and the range i

1. **State the problem:** We need to graph the function $$y = 5|x - 2| - 7$$ and identify its vertex. 2. **Recall the formula and rules:** The function is an absolute value functio

1. **State the problem:** Solve for $y$ in the equation $$\frac{y + 4}{6y} - \frac{4}{9} = \frac{1}{y}.$$\n\n2. **Identify the common denominator:** The denominators are $6y$, $9$,

1. **State the problem:** Solve the equation $$\frac{2}{u} + \frac{1}{6} = \frac{7}{6u}$$ for $u$. 2. **Identify the common denominator:** The denominators are $u$, $6$, and $6u$.

1. **State the problem:** Solve the equation $$\frac{5}{2w - 3} - \frac{7}{7w} = 1$$ for $w$. 2. **Identify the common denominator:** The denominators are $2w - 3$ and $7w$. The co

1. **State the problem:** We are given a rectangle where the length is three times the width, and the area is 147 cm². We need to find the perimeter. 2. **Define variables:** Let t

1. **State the problem:** We need to find the area of a rectangle where the length is 5 inches longer than the width, and the perimeter is 34 inches.

1. **State the problem:** Solve the equation $$\frac{7w}{w+2} - 8 = \frac{3w}{w+2}$$ for $w$. 2. **Identify the formula and rules:** This is a rational equation where terms have de

1. **State the problem:** Solve the equation $$2 + \frac{4}{y - 4} = \frac{6}{y - 4}$$ for $y$. 2. **Identify the domain:** The denominator $y - 4$ cannot be zero, so $y \neq 4$.

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

1. **State the problem:** We are given two functions: $g(x) = x + 3$ and $h(x) = x^2$. We need to calculate: (i) $g(-5)$

1. **State the problem:** Find the slope of the line passing through the points $(-21, -41)$ and $(-22, -9)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)

1. **State the problem:** Find the slope of the line passing through the points $(29, 86)$ and $(99, 14)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)$ a

1. **State the problem:** You want to understand how to decide which number to divide both sides of an equation by when solving for a variable. 2. **General rule:** When you have a

1. **State the problem:** Simplify the expression $$\left(\frac{z^6}{4ab^{-2}}\right) \left(3a^2 b^5\right)^2$$. 2. **Recall the rules:**

1. **State the problem:** We want to find the percentage $x$ such that 15.5 is $x\%$ of 77.5. 2. **Formula used:** The general formula to find $x\%$ of a number is: