🧮 algebra

1. **State the problem:** We are given two functions:

1. **State the problem:** Solve the compound inequality $$k - 10 \leq -5 \text{ or } k - 11 \geq -4$$ for $k$. 2. **Solve the first inequality:**

1. **State the problem:** Simplify the expression $$\sqrt{75y^7}$$ assuming $$y \geq 0$$. 2. **Recall the property of square roots:** $$\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$$

1. **State the problem:** We have four linear functions and need to answer three questions about their y-intercepts and slopes. 2. **Identify y-intercepts and slopes:**

1. The problem asks for the expression representing the total volume of a box with dimensions given by the expressions $(x + 2)$, $(2x - 1)$, and $(3x + 1)$. The volume of a box is

1. The problem is to find the value of $A$ in the vertical multiplication of the polynomials $(4a^3 - 2a + 3a^2 + 1)$ and $(3 - 2a + a^2)$. 2. The vertical multiplication method in

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:** $a(b - c) = ab - ac$.