🧮 algebra

1. **State the problem:** Solve for $x$ in the linear equation $$3(2x + 4) = 18$$. 2. **Use the distributive property:** Multiply 3 by each term inside the parentheses:

1. **State the problem:** Find the domain of the function $$f(x) = \frac{x-4}{x^3 - 16x}$$. 2. **Recall the domain rule for rational functions:** The domain includes all real numbe

1. **State the problem:** Factor the expression $$x^3 - 16$$. 2. **Recognize the form:** This is a difference of cubes because $$16 = 2^4$$ is not a perfect cube, but we can rewrit

1. **State the problem:** We need to find how many Basic ($x$) and Advanced ($y$) products to manufacture so that the Assembly and Finishing departments run at full capacity.

1. **State the problem:** We have a concert hall with a total of $1250$ seats.

1. **State the problem:** We have two equations: $$6x + b = x - 2$$

1. **State the problem:** We have two linear equations: $$5x + b = 3x - 9$$

1. **State the problem:** We need to plot points for the linear equation $$y = -\frac{1}{2}x - 9$$ and connect them with a line. 2. **Formula and rules:** The equation is in slope-

1. **State the problem:** We need to plot points on the coordinate grid for the line given by the equation $$y = -3x - 6$$ and connect these points with a line. 2. **Formula and ru

1. **Problem:** Calculate the product $(-\frac{1}{2}) \cdot (+\frac{2}{3}) \cdot (-\frac{3}{4}) \cdot (-\frac{4}{5}) \cdot (-\frac{5}{6})$. 2. **Formula and rules:** When multiplyi

1. **State the problem:** We need to find the values of $a$ such that the coefficient of $x^3$ in the expansion of $$\left(2x + \frac{1}{ax^2}\right)^9$$ is 288. 2. **Recall the bi

1. **State the problem:** Find the equation of the line passing through the point $(-2, 1)$ and parallel to the line $y= \frac{4}{3} x + 7$. 2. **Recall the formula for a line para

1. **State the problem:** Find the equation of the line passing through the point $(0, 2)$ and parallel to the line $y = -2x - 1$. 2. **Recall the formula:** The equation of a line

1. **State the problem:** We need to determine which of the given sets of ordered pairs represents a function. 2. **Recall the definition of a function:** A set of ordered pairs is

1. **State the problem:** We need to determine which of the given sets of ordered pairs represents a function. 2. **Recall the definition of a function:** A set of ordered pairs is

1. **Stating the problem:** We want to prove and explain why the sum of fractions $$\frac{1}{n+1} + \frac{1}{n+2} + \cdots + \frac{1}{2n}$$ is greater than $$\frac{13}{24}$$ for so

1. **State the problem:** We are given the function $$f(x) = \frac{x + 5}{2}$$ and need to evaluate it for different inputs: $$-1$$, $$44$$, $$z - 5$$, and $$5z$$. 2. **Formula use

1. **State the problem:** Convert the decimal number $0.004$ to a percentage. 2. **Formula used:** To convert a decimal to a percentage, multiply the decimal by 100 and add the per

1. **State the problem:** We need to find the product of the two polynomials $6x^5 - 2x^3$ and $x^4 - 3x$. 2. **Formula and rules:** To multiply two polynomials, use the distributi

1. **State the problem:** We need to find the product of the two polynomials $2x^4 + 3x^2$ and $x^4 - x^2$. 2. **Formula used:** To multiply two binomials, use the distributive pro

1. **Problem:** Calculate $0.8 - 0.206$. **Step 1:** Write the subtraction.