🧮 algebra

1. **State the problem:** We need to find the domain and range of the given function, determine if it is invertible, justify the invertibility, and if invertible, find the domain a

1. **State the problem:** We need to evaluate the expression where the first two rational numbers are added instead of multiplied. Suppose the original expression was $\frac{a}{b}

1. **State the problem:** Simplify the expression $$\frac{x^2 - 5x + 6}{x^2 - 4x - 5} \times \frac{x^2 - 5}{x^2 + 3x + 2}$$. 2. **Factor all polynomials:**

1. **State the problem:** Find the equation of the normal to the function $f(x) = ax^2 + bx + c$ at the turning point. 2. **Recall the turning point:** The turning point of a quadr

1. **Problem:** Write the ratio 75 to 100 in simplest form. 2. **Formula:** To simplify a ratio, divide both terms by their greatest common divisor (GCD).

1. **State the problem:** Solve the equation $4x = 76$ for $x$. 2. **Formula and rule:** To solve for $x$, divide both sides of the equation by the coefficient of $x$, which is 4.

1. **State the problem:** Solve for $x$ in the equation $\frac{x}{3} = 16$. 2. **Formula used:** To isolate $x$, multiply both sides of the equation by 3 because $x$ is divided by

1. **State the problem:** Solve for $x$ in the equation $73 + x - 1 + x = 180$.

1. **State the problem:** Solve the inequality $$-1 - (-4x + \frac{5}{2}) - 3x \leq -\frac{1}{2}x$$. 2. **Distribute the negative sign inside the parentheses:**

1. The problem is to simplify the expression $-\frac{6}{5}$ or understand its value. 2. The expression $-\frac{6}{5}$ is a fraction with a negative sign in front, meaning the value

1. **State the problem:** Solve the inequality $$-3 > \frac{6}{5}(-2x - 1) - 1$$. 2. **Distribute the fraction:** Multiply $$\frac{6}{5}$$ by each term inside the parentheses:

1. **State the problem:** Solve the inequality $$-7x - \left(-5x + \frac{1}{4}\right) \leq -1$$. 2. **Apply the distributive property:** Remove the parentheses by distributing the

1. **State the problem:** Solve the inequality $$3 \leq 1 + 6 \left(-4x - \frac{5}{3}\right)$$. 2. **Distribute the 6:** Multiply 6 by each term inside the parentheses:

1. **State the problem:** Students are selling tickets at 11 each to raise money for a dance. They already have 450 from the PTO and need at least 1110 total to cover costs. We wan

1. **State the problem:** Solve the inequality $$5 + 9x < - \frac{1}{2}x - \left( \frac{3}{2}x + 1 \right)$$. 2. **Distribute the negative sign on the right side:**

1. **State the problem:** Jordan has 80 tickets. He wants to buy a bag of popcorn that costs 24 tickets and use the remaining tickets to play games. Each game requires 4 tickets. W

1. **State the problem:** Solve the system of equations by substitution: $$y = -7x + 10$$

1. **State the problem:** Solve the equation $5(x + 3) = 4(2x - 14) - 1$ for $x$. 2. **Write down the equation:**

1. **State the problem:** Calculate $13543^4$. 2. **Formula used:** To find the power of a number, multiply the number by itself as many times as the exponent indicates. Here, $135

1. The problem is to calculate $1232938348^{100}$. 2. The formula for exponentiation is $a^n = a \times a \times \cdots \times a$ ($n$ times).

1. **State the problem:** You want to graph the linear equation $y = 8x + 86$ which represents the number of alabers $y$ after $x$ hours.