🧮 algebra

1. **State the problem:** We want to subtract the fractions $\frac{5}{x}$ and $\frac{2x + 10}{x}$.\n\n2. **Look at the denominators:** Both fractions have the same denominator $x$,

1. **State the problem:** Simplify the expression $$\frac{5}{x} - \frac{2x + 10}{x}$$. 2. **Identify the common denominator:** Both terms have the denominator $x$, so we can combin

1. **State the problem:** We are given a relation M with points $(x, y)$ as follows: $(-1, 3)$, $(0, 6)$, $(2, 12)$, and $(3, 15)$. We need to determine the nature of the rate of c

1. **Problem:** Determine which pair of points shows a graph that is not a function. 2. **Recall the definition of a function:** A graph represents a function if every input (x-val

1. **Problem statement:** Three fifths of those present agreed, and the remaining 12 disagreed. Find: a. The fraction of those who disagreed.

1. **State the problem:** We have the function $$f(x) = \frac{\lfloor x \rfloor + x}{2}$$ where $$\lfloor x \rfloor$$ is the greatest integer less than or equal to $$x$$. We want t

1. **State the problem:** Simplify the expression $$\frac{x^4 + 8x^3 + 24x^2 + 32x + 16}{x^3 + 6x^2 + 12x + 8}$$ and determine its domain. 2. **Recognize the polynomials:** Both nu

1. **State the problem:** We are given the linear function $$y = \frac{2}{3}x - 5$$ and a table with values of $$x$$: -9, 0, 3, 6. We need to find the corresponding values of $$y$$

1. Stating the problem: Simplify the expression $$a^{-7} b^{2} c^{-1} = \frac{2 n^{-5} p^{0}}{m^{-2}}$$. 2. Recall the rules of exponents:

1. **State the problem:** Simplify the expression $$2x^{8}y^{15} - \frac{40x^{10}y^{24}}{5x^{2}y^{9}}$$. 2. **Recall the rules:**

1. The problem is to convert the improper fraction $\frac{33}{28}$ into a mixed number. 2. An improper fraction has a numerator larger than the denominator. To convert it, divide t

1. **State the problem:** Match each situation (a, b, c, d) to one of the graphs (A, B, C) based on the description of the graph and the situation. 2. **Analyze each graph:**

1. The problem is understanding why the factorial expression $(N+1)!$ remains as is, instead of simplifying to $(N+1) - 1$. 2. Recall the definition of factorial: for any positive

1. **State the problem:** Simplify and solve the equation $\frac{x+x+x}{x} = 10$. 2. **Understand the expression:** The numerator is $x+x+x$, which is $3x$.

1. **State the problem:** Factor the expression $$9x^2 - 16$$ completely. 2. **Recognize the form:** This is a difference of squares, which follows the formula $$a^2 - b^2 = (a - b

1. **State the problem:** Show that $k \times k! = (k + 1)! - k!$ and then use this to sum the series $1 \times 1! + 2 \times 2! + 3 \times 3! + \cdots + n \times n!$.

1. **State the problem:** Factor the expression $$9x^2 - 16$$ completely. 2. **Recognize the form:** This is a difference of squares because $$9x^2 = (3x)^2$$ and $$16 = 4^2$$.

1. **State the problem:** We need to evaluate the expression $\left(3(5)-4(-2)\right)^2$. 2. **Apply the order of operations:** First, calculate the products inside the parentheses

1. **State the problem:** Simplify the expression $$2j(7j^2k^2 + jk^2 + 5k) - 9k(-2j^2k^2 + 2k^2 + 3j)$$. 2. **Distribute each term:**

1. **State the problem:** Ethan earned 188.40 for 12 hours of work. We need to find how much he earned per hour. 2. **Formula:** The unit rate (earnings per hour) is calculated by

1. **State the problem:** Solve the equation $$\frac{x}{6} = 4$$ for $x$. 2. **Recall the formula:** To solve for $x$ when it is divided by a number, multiply both sides of the equ