🧮 algebra

1. The problem is to divide 5 by $\frac{1}{2}$, i.e., calculate $5 \div \frac{1}{2}$. 2. The rule for division by a fraction is to multiply by its reciprocal. That means:

1. **State the problem:** We have a piecewise function $$f(x) = \begin{cases} \frac{x \sqrt{x}}{x-2} & x < 2 \\ \frac{(x^2 - 2)^2}{(x^2 - 2)^2} & x \geq 2 \end{cases}$$

1. **State the problem:** We have the function modeling the number of playgrounds built, $n$, in terms of dollars raised, $r$:

1. **State the problem:** Find the inverse function of the model $$n = \frac{848r}{1000} - 1525$$ where $n$ is the number of playgrounds built and $r$ is the amount of money raised

1. **State the problem:** Solve the equation $4(x-3)-3(x-5)=3(x+1)$ for $x$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside

1. The problem is to understand the variable $h$ and its role or value. 2. Since the message only states "its h" without additional context, we interpret $h$ as a variable, often u

1. **State the problem:** We need to find the equation of a line in slope-intercept form $y=mx+b$ given the slope $m=-15$ and a point on the line $(-5,7)$. 2. **Recall the slope-in

1. **State the problem:** We want to understand how to express and work with the expression \( \frac{12}{x} \). 2. **Formula and explanation:** The expression \( \frac{12}{x} \) me

1. **State the problem:** Solve the equation $$(2x+3)^2 = 12x$$ for $x$. 2. **Use the formula:** Recall that $$(a+b)^2 = a^2 + 2ab + b^2$$.

1. **State the problem:** Simplify the expression $96 - 28 (1 - 6 \div 9) \times 22 - 8 \times 3$. 2. **Recall the order of operations (PEMDAS/BODMAS):**

1. **State the problem:** Solve the inequality $$\frac{x}{9} - \frac{x}{7} < 0$$ and determine which option about $x$ is correct. 2. **Find a common denominator:** The denominators

1. **State the problem:** Solve the equation $$-6 + \frac{x}{2} = -3$$ for $x$. 2. **Isolate the variable term:** Add 6 to both sides to move the constant term.

1. **State the problem:** Solve the inequality $$\frac{x}{9} - \frac{x}{7} < 0$$. 2. **Find a common denominator:** The denominators are 9 and 7, so the common denominator is $$63$

1. **State the problem:** Evaluate the expression $5^2 - (7 - 2 \times 3)$. 2. **Recall order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplication and Division from

1. **State the problem:** Evaluate the expression $5^2 - (7 - 2 \times 3)$. 2. **Recall order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplication and Division (left

1. **State the problem:** Simplify the expression $9 - 3(9 - 3)$. 2. **Recall the order of operations:** Parentheses first, then multiplication, then addition/subtraction from left

1. The problem is to find the value of the given expression or quantity. 2. Since the user did not specify the exact expression, we need the expression to proceed.

1. **State the problem:** We need to find the equation that represents the proportional relationship between the number of pencils $p$ and the cost $c$ given the data points: $(9,

1. **State the problem:** We want to find the share of the customer's wallet spent at your store compared to the total amount spent on flower arrangements. 2. **Identify the given

1. Stating the problem: Solve the equation $$|x - |x|| = 10$$. 2. Understand the absolute value function: $$|x| = \begin{cases} x & \text{if } x \geq 0 \\ -x & \text{if } x < 0 \en

1. **State the problem:** Write an equation that represents the proportional relationship between the price $P$ of canned corn and the number of cans $c$ purchased. 2. **Analyze th