🧮 algebra

1. **State the problem:** Calculate the value of the expression $$-8 \cdot 45 \div 9$$. 2. **Recall the order of operations:** Multiplication and division are performed from left t

1. **State the problem:** Factor fully the expression $3xy + 3xz + 2y + 2z$. 2. **Group terms:** Group terms to find common factors:

1. **State the problem:** Factor the quadratic expression $x^2 - 5x + 6$ fully. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that m

1. Gegeben ist die lineare Gleichung: $$6(3x + 2) = -24$$ 2. Zuerst wenden wir das Distributivgesetz an, um die Klammer aufzulösen:

1. Gegeben ist die lineare Gleichung: $$2(3x + 2) = 13$$ 2. Zuerst wenden wir das Distributivgesetz an, um die Klammer aufzulösen:

1. The problem is to analyze the system of inequalities: $$y > -x - 2$$

1. **State the problem:** We have a piecewise function for a car-sharing service membership fee:

1. **State the problem:** Simplify the expression $ (f \cdot g^2) + 5 - (g^2 \cdot f) $ to an equivalent expression with only one term. 2. **Identify like terms:** Notice that $ f

1. Problem 28: Write an algebraic expression for the area of a rectangular rug and find an equivalent expression using properties of operations. The area $A$ of a rectangle is give

1. The problem asks if soccer balls cost 2 1/2 times as much as baseballs. 2. First, convert the mixed number 2 1/2 to an improper fraction: $$2 \frac{1}{2} = \frac{5}{2}$$.

1. **Stating the problem:** We are given several algebraic expressions and word problems involving variables and constants. We need to simplify expressions and write algebraic expr

1. Problem: Write expressions for the length of red and blue ribbons based on given conditions. 2. The problem states: The length of the red ribbon is 7 inches less than the length

1. **Problem Statement:** We need to write an equation representing the relationship between the amount of water $W$ (in liters) and time $T$ (in minutes) for filling a fish tank.

1. **Problem Statement:** We are given a graph showing the relationship between the amount of water $W$ (in liters) in a fish tank and the time $T$ (in minutes) since the tank star

1. **State the problem:** Simplify the expression $20n - 4m = 4(n - m)$. 2. **Recall the distributive property:** $a(b - c) = ab - ac$.

1. **State the problem:** Simplify and solve the expression $3(m + 3) = 3m + 3$. 2. **Use the distributive property:** Multiply 3 by each term inside the parentheses.

1. **State the problem:** We have a tape diagram with three equal parts, each labeled 9, and the total length is 27. 2. **Write the equation using addition:** Since the total is th

1. **Stating the problem:** Solve the quadratic equation $x^2 - 5x + 6 = 0$. 2. **Formula used:** The quadratic formula is given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where

1. **State the problem:** Solve the quadratic equation $ax^2 + bx + c = 0$ where $a \neq 0$. 2. **Formula used:** The quadratic formula to find roots is

1. **State the problem:** Solve the inequality $18 + 0.04m \geq 76.08$ for $m$. 2. **Isolate the variable term:** Subtract 18 from both sides to get

1. **State the problem:** We need to find the equation of the secant line passing through the points $(-4, h(-4))$ and $(2, h(2))$ where $h(x) = x^3 + 6$. 2. **Calculate the functi