🧮 algebra

1. Let's start by stating the problem: You want answers for practice questions and explanations on how to solve them. 2. Since no specific questions were provided, I'll demonstrate

1. **State the problem:** We need to simplify the expression $$\frac{9}{2} + \frac{11}{3} + \frac{17}{6} = ? + \frac{12}{5} + \frac{21}{10}$$ and find the value of the unknown term

1. Solve each inequality in section 2 step-by-step. (a) Solve $5x - 6 < 29$:

1. **State the problem:** We have a sequence where each term is found by multiplying the previous term by 4 and then subtracting 31. 2. **Given:** The 9th term, $a_9 = 25$. We want

1. The point-slope form of a line is used primarily to write the equation of a line when you know a point on the line and the slope of the line. 2. The formula for the point-slope

1. The problem is to find the upper and lower boundaries for the number 6. 2. Upper and lower boundaries refer to the smallest and largest numbers that round to 6 under a certain r

1. **State the problem:** Find the equation of the line parallel to the line given by $$3x + y - 4 = 0$$ that passes through the point $$(2, -5)$$. 2. **Identify the slope of the g

1. We are given the system of inequalities: $$-4x^2 + x - 6 < 0$$

1. **State the problem:** We need to find the values of $\alpha$ and $b$ given the system of equations: $$12 = 8 + \alpha$$

1. **State the problem:** Solve the equation $60 = 10y$ for $y$. 2. **Formula and rules:** To solve for $y$, we need to isolate $y$ on one side of the equation. Since $y$ is multip

1. **State the problem:** Solve the linear equation $3x - 1.5 = 10.5$ for $x$. 2. **Recall the formula and rules:** To solve for $x$, isolate $x$ on one side of the equation by per

1. **State the problem:** Solve the equation $n - 11 = 16$ for $n$. 2. **Formula and rules:** To solve for $n$, we want to isolate $n$ on one side of the equation. We do this by pe

1. **State the problem:** Simplify the expression $$(6-\frac{3}{w})^2$$. 2. **Formula used:** The square of a binomial $$(a-b)^2 = a^2 - 2ab + b^2$$.

1. The problem asks for the coordinates of the y-intercept of the quadratic function. 2. The y-intercept of a function is the point where the graph crosses the y-axis. This occurs

1. **Stating the problem:** Simplify the expression $6 - \frac{3}{w^2}$. 2. **Formula and rules:** When subtracting a fraction from a whole number, treat the whole number as a frac

1. **State the problem:** Solve the linear equation $$22 - 8x = 2x + 9$$. 2. **Write down the formula and rules:** To solve for $x$, we want to isolate $x$ on one side of the equat

1. **State the problem:** We have a function $$f(x) = a(x + 2)(x - a)(x - 8)$$ where $$a$$ is a constant. We want to find which value of $$a$$ makes $$f(2.5)$$ negative. 2. **Subst

1. **State the problem:** We need to calculate $1 \frac{2}{7} \div \frac{2}{7}$ and express the answer as a simplified fraction. 2. **Convert mixed number to improper fraction:**

1. **Problem statement:** Find the number of distinct real values of $x$ such that $$(x^2 - 4)(x - 4)^2(x^2 + 4) = 0.$$ 2. **Formula and rules:** A product of factors equals zero i

1. **State the problem:** We want to find the number of distinct positive integers $n$ such that the product $(n-1)(n-9)(n-17)$ is less than 0. 2. **Understand the expression:** Th

1. **State the problem:** Solve the equation $$6 = x + \frac{3}{x}$$ for $x$. 2. **Rewrite the equation:** Multiply both sides by $x$ (assuming $x \neq 0$) to eliminate the fractio