🧮 algebra

1. **State the problem:** We are given the function $$f(x) = \frac{x+1}{6x^2 - 7x - 3}$$ and need to determine whether the points $$x=\frac{3}{2}, x=-\frac{1}{3}, x=-\frac{3}{2},$$

1. State the problem: Simplify fully the expression $3(2x - 5) - 4(x + 1)$.\n\n2. Apply the distributive property: Multiply each term inside the parentheses by the factor outside.\

1. Problem statement: The price of an item is 3000 in the year 2023. The price is expected to increase by 3% per year. We define $x$ as the number of years after 2023 and $p(x)$ as

1. **State the problem:** Solve the compound inequality $$-4 \leq \frac{1}{2}(8x + 8) < 12$$ and find the solution set. 2. **Recall the rule:** When solving inequalities, you can m

1. **State the problem:** We have a Fibonacci-type sequence where each term is the sum of the two previous terms. The sequence is: $a_1$, 5, $a_3$, $a_4$, 23, ...

1. **State the problem:** Simplify fully the expression $3(2x - 5) - 4(x + 1)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outs

1. **Stating the problem:** We need to find the value of the sum $$\frac{1}{\sqrt{1} + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \cdots + \frac{1}{\sqrt{35} + \sqrt{36}}$$

1. **State the problem:** Simplify the expression $$\frac{(3m^{-2} n)^{-3}}{6mn^{-2}}$$ assuming $$m \neq 0$$ and $$n \neq 0$$. 2. **Recall the rules:**

1. **State the problem:** Solve the inequality $$2 - \frac{m}{11} \leq -7$$ and determine the solution set. 2. **Isolate the variable term:** Subtract 2 from both sides:

1. **State the problem:** We need to find the percentage decrease in the world record time between February 2013 and March 2013. 2. **Convert times to seconds:**

1. **State the problem:** We need to find the starting value of Hattie's house given that after one year it increased by 9%, and after the second year it decreased by 4%, resulting

1. Problemet handlar om funktionen $f(x) = 0{,}3 + 0{,}5 e^{-0{,}76x}$ där $f(x)$ är bensinförbrukningen i liter per mil och $x$ är sträckan i mil från start. 2. Funktionen beskriv

1. **State the problem:** Simplify the expression $\left(5^{-1}\right)\left(5^{-3}\right)$. 2. **Recall the exponent multiplication rule:** When multiplying powers with the same ba

1. **State the problem:** Factor the expression $$q^4 + 3q^2 - 10$$ into two binomials. 2. **Identify the structure:** Notice that $$q^4$$ is $$\left(q^2\right)^2$$, so treat $$q^2

1. **State the problem:** Simplify the expression $$\frac{3x^{-6}y^{-3}}{15x^{2}y^{10}}$$ assuming $$x \neq 0$$ and $$y \neq 0$$. 2. **Recall the rules:**

1. **State the problem:** We need to find the number of extraneous solutions for the equation $$\frac{2m}{2m+3} - \frac{2m}{2m-3} = 1$$. 2. **Identify restrictions:** The denominat

1. **State the problem:** We need to graph the inequality $$y \geq \frac{3}{2}x - 6$$ on a Cartesian coordinate plane. 2. **Understand the inequality:** The inequality means we wan

1. Problem: Simplify $y^5 \cdot y^7$. Step 1: Use the product of powers rule: $a^m \cdot a^n = a^{m+n}$.

1. The problem is to simplify the algebraic expression: 4(x + 7) = (4F1) X 2. First, we interpret the expression 4(x + 7). This means multiplying 4 by each term inside the parenthe

1. **Problem Statement:** Check the exponent properties and simplifications given in the quiz. 2. **Reviewing each step:**

1. The problem is to find the percentage of 2 with respect to 7. 2. The formula to find the percentage of a number $a$ with respect to another number $b$ is: