🧮 algebra

1. Let's analyze each sequence to find the rule. 2. Sequence 1: 5, 10, 14, 16, 18

1. **State the problem:** Solve the equation $$\frac{x+3}{x-2} = \frac{x-2}{x+3}$$. 2. **Cross-multiply to eliminate the fractions:**

1. **State the problem:** We have a balance scale with three 3's on one side and three unknown weights represented by square brackets and a circle on the other side. We want to mod

1. **State the problem:** Solve the inequality $$\frac{x}{x-2} + \frac{x}{x^2-4} \leq 0$$ using the graph of $$f(x) = \frac{x}{x-2} + \frac{x}{x^2-4}$$. 2. **Rewrite the function:*

1. **State the problem:** We need to analyze the inequality $$\frac{5}{x^2 + 1} \leq 1$$ and find the values of $x$ that satisfy it. 2. **Rewrite the inequality:** Since $x^2 + 1 >

1. **State the problem:** We have a balance scale with 3 identical squares on the left side and 1 triangle plus 3 identical circles on the right side. We want to model this situati

1. **State the problem:** Solve the equation $$\frac{x - 2}{x^2 + x - 1} = \frac{1}{x - 3}$$ for $x$. 2. **Recall the formula and rules:** To solve an equation with fractions, we c

1. **Stating the problem:** We have three rows of shapes representing an algebraic equation. Each shape corresponds to a variable: let the square be $S$, the triangle be $T$, and t

1. The problem is to simplify the expression $7 - 2 \times 6$. 2. According to the order of operations (PEMDAS/BODMAS), multiplication is performed before subtraction.

1. **State the problem:** Simplify the expression $8 - 3(5 - 3^2)$. 2. **Recall the order of operations:** Parentheses, exponents, multiplication/division, addition/subtraction (PE

1. **State the problem:** Solve the system of equations using elimination: $$-4x - 9y = 26$$

1. The problem is to choose the correct first step to eliminate a variable in the system of equations: $$-4x - 4y = -68$$

1. **State the problem:** Find the shortest route from Kingwood to Richmond using the given paths and distances. 2. **List the paths and distances:**

1. **State the problem:** Find the number of combinations of nickels and dimes that total 80 cents using exactly 11 coins. 2. **Define variables:** Let $n$ be the number of nickels

1. **State the problem:** Find the number of combinations of nickels (5 cents) and quarters (25 cents) that total 80 cents using exactly 11 coins. 2. **Define variables:** Let $n$

1. **Problem:** Find the inverse of the function $f(x) = 2x - 3$ and state if the inverse is a function, one-to-one function, or neither. 2. **Formula and rules:** To find the inve

1. **State the problem:** Find the number of combinations of nickels (5 cents) and quarters (25 cents) that total 80 cents using exactly 10 coins. 2. **Define variables:** Let $n$

1. **Problem:** Find the inverse of the function $f(x) = 2x - 3$ and determine if the inverse is a function, one-to-one function, or neither. 2. **Formula and rules:** To find the

1. **State the problem:** Find another combination of nickels ($x$) and dimes ($y$) that totals 11 coins and equals 0.80 in value. 2. **Recall the equations:**

1. **State the problem:** Zendaya has nickels and dimes totaling 11 coins, worth 0.80 dollars. We want to find the number of nickels $x$ and dimes $y$. 2. **Set up equations:**

1. **State the problem:** Evaluate the expression $4 \frac{1}{2} \times \left(-\frac{2}{3}\right) + \frac{7}{8}$. 2. **Convert the mixed number to an improper fraction:**