🧮 algebra

1. Stating the problem: Solve the equation $a x - 4 = 10$ for $x$. 2. Add 4 to both sides to isolate the term with $x$:

1. **Problem Statement:** Find the inverse function $f^{-1}$ of $f(x) = 3x$, check the answer, and find the domain and range of both $f$ and $f^{-1}$. Also, graph $f$, $f^{-1}$, an

1. **State the problem:** Factorize the quadratic expression $2x^2 + 6x + 4$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that mul

1. **State the problem:** Simplify the expression $$\frac{-3 + (-2 - 9) - 1}{(-5)(-2 - 3 + 6)}$$. 2. **Simplify the numerator:**

1. **State the problem:** Mary sells $28,000 worth of furniture and has already received a draw of $766.15. We need to calculate how much commission is still owed to her based on t

1. **State the problem:** Simplify the expression $$9q^2 + 6q^2 + 12p^3 + 3p^3 + 18q^2$$. 2. **Identify like terms:** Terms with the same variable and exponent can be combined.

1. The problem asks to find $(f - g)(x)$ given $f(x) = 7x - 6$ and $g(x) = 2x - 4$. 2. The formula for the difference of two functions is:

1. **State the problem:** Pamela Mello earns a commission of 2.6% on the first 70000 and 3.4% on any sales above 70000. Her weekly sales are 86800. We need to find her total commis

1. **Stating the problem:** We want to find a function that models the number of students participating in sports after $x$ years, given that the initial number is 317 and it incre

1. **State the problem:** A customer buys an electronic device for 650. Each year, its value decreases by 39%. We want to determine which statement about the graph of the device's

1. **State the problem:** Determine which statement about the graph of the function $y = 16(0.5)^x$ is NOT true. 2. **Recall the function and its properties:** The function is an e

1. **State the problem:** Simplify the expression $2a\sqrt{3} - \sqrt{27a^2} + a\sqrt{12}$. 2. **Recall the rules:**

1. **Problem:** Find the equation of a straight line with gradient $m$ passing through a point $(x_1, y_1)$. 2. **Formula:** The point-slope form of a line is given by:

1. **Problem:** Factor the polynomial $4x^2 - 1$ using a special pattern. 2. **Formula and rules:** This is a difference of squares pattern: $$a^2 - b^2 = (a - b)(a + b)$$ where $a

1. **State the problem:** Simplify the expression $$\sqrt[3]{512x^4 y^5}$$. 2. **Recall the cube root properties:** The cube root of a product is the product of the cube roots: $$\

1. **State the problem:** Simplify the expression $$(4 \times \sqrt{18x}) (6 \sqrt{6x})$$. 2. **Recall the properties of square roots and multiplication:**

1. The problem appears to involve understanding the relationship between the numbers given: $4 = 24$, $- 6 = 4$, and $= 4 \times 6$. We need to clarify what is being asked, but sin

1. **State the problem:** Simplify the expression $\frac{y}{12x^5} + \frac{5}{9x^2}$. 2. **Find a common denominator:** The denominators are $12x^5$ and $9x^2$. The least common de

1. **Problem Statement:** Simplify the complex rational expression. For example, simplify $$\frac{\frac{a}{b} + \frac{c}{d}}{\frac{e}{f} - \frac{g}{h}}$$. 2. **Formula and Rules:**

1. Stating the problem: Simplify the expression $3(m+n)^2$. 2. Recall the formula for the square of a binomial: $$(a+b)^2 = a^2 + 2ab + b^2$$

1. **State the problem:** Simplify the expression $$\frac{e^3 - \ln(4)}{3 + e \sqrt{e + 1 + \pi}} - 4e$$. 2. **Recall the components:**