🧮 algebra

1. **State the problem:** Solve the equation $ (x - 9)(x + 2) = (x + 4)(x - 7) $ for $x$. 2. **Expand both sides:** Use the distributive property (FOIL) to expand each product.

1. **State the problem:** Solve the inequality $$\frac{x}{4} > 8$$. 2. **Formula and rules:** To solve inequalities involving fractions, multiply both sides by the denominator to e

1. **State the problem:** Solve for $x$ in the equation $4^x = 256$. 2. **Recall the formula and rules:** We know that $a^m = a^n$ implies $m = n$ if the bases $a$ are the same.

1. **State the problem:** Simplify the expression $\log_9 3 + \log_9 27$. 2. **Recall the logarithm property:** The sum of logarithms with the same base is the logarithm of the pro

1. **Problem Statement:** Determine the cost for Nancy to have Saxony carpeting installed in all three bedrooms, given the cost is $7.49 per square foot. 2. **Formula:** Total cost

1. **State the problem:** Simplify the expression $$\frac{8m^6n^2}{4m^3} \cdot \frac{12(mn)^3}{n^2}$$ and write an expression for the area of a rectangle with dimensions $$(2a^2 b)

1. **State the problem:** Simplify the expression $$\frac{\left(-2 m^{-5} n^{4}\right)^{-2}}{\left(3 m^{8} n^{-4}\right)^{-1}}.$$\n\n2. **Recall the rules:**\n- Power of a product:

1. **State the problem:** We are given a system of three equations:

1. **State the problem:** We need to select the equation that best represents the first model (bottom-left) where the scale has one star on the left and three rectangles on the rig

1. **State the problem:** Simplify the expression $$(9m^{\frac{5}{3}})(4m^{-\frac{7}{2}})$$. 2. **Use the product rule for exponents:** When multiplying terms with the same base, a

1. **State the problem:** Simplify the expression $$\frac{\sqrt{y^7} \times \sqrt[5]{y^2}}{\sqrt[5]{y^4}}$$. 2. **Rewrite roots as exponents:** Recall that $$\sqrt{y^7} = y^{\frac{

1. The problem asks to describe each given roster (list of elements) using set-builder notation. 2. Set-builder notation describes a set by stating the properties that its members

1. The problem is to create a table of values and graph the linear function $y = -x + 4$. 2. The formula for a linear function is $y = mx + b$, where $m$ is the slope and $b$ is th

1. **State the problem:** Simplify the expression $$\left(\frac{100a}{25a^{2}b^{\frac{1}{2}}}\right)^{-\frac{1}{2}}$$. 2. **Recall the rules:**

1. **State the problem:** We are given a graph of a function $f(x)$ which is a straight line descending from top left to bottom right. 2. **Identify key points from the graph:** Th

1. **State the problem:** Solve the equation $$-\frac{1}{2}x - 3 = 4$$ for $x$. 2. **Add 3 to both sides** to isolate the term with $x$:

1. **State the problem:** We are given the equation $c = 3 + n$, which represents the number of coins $c$ a player has after winning $n$ levels in a video game. 2. **Understand the

1. The problem states that the number of coins $c$ a player has after winning $n$ levels is given by the equation $$c = 3 + n.$$ 2. We are asked to find how many coins the player s

1. **State the problem:** Solve the system of equations: $$\frac{x}{10} + \frac{y}{20} = 4$$

1. **Problem:** Find the values of the following logarithms to four decimal places using the property of logarithms and the given table values. 2. **Formula and rules:**

1. **State the problem:** Factor the expression $$242f^2 - 32$$ completely. 2. **Identify the type of expression:** This is a difference of two terms, which can be factored using t