🧮 algebra

1. **State the problem:** Solve for $x$ in the equation $5(9-4) + x(2-5) = 0$. 2. **Apply the distributive property:** Calculate the values inside the parentheses.

1. **State the problem:** Solve the equation $-8(x-3)+4=4(-x+8)-4x$ for $x$. 2. **Apply the distributive property:**

1. **State the problem:** Solve the equation $3(a+2)-2a=\frac{1}{7}(-7a+42)$. 2. **Write down the equation:**

1. **State the problem:** Solve the equation $$\frac{7x - 2}{4} = 3x + 1$$ for $x$. 2. **Formula and rules:** To solve for $x$, we want to isolate $x$ on one side. Since $x$ is ins

1. **State the problem:** Solve the equation $5(K+4) = 2(2.5K - 3) + 12$ for $K$. 2. **Write the formula and rules:** Use the distributive property to expand both sides and then is

1. **State the problem:** Simplify the expression $28y^2 - 21y$. 2. **Identify the common factors:** Both terms have a common factor of 7 and a factor of $y$.

1. **State the problem:** Solve the equation $5(K+4) = 2(5K-3) + 12$ for $K$. 2. **Write the formula and rules:** Use the distributive property to expand both sides and then isolat

1. **State the problem:** Expand and simplify the expression $$(x + 7)(x - 2)$$. 2. **Formula used:** Use the distributive property (also called FOIL for binomials):

1. **State the problem:** Expand and simplify the expression $$3(c - 7) + 2(3c + 4)$$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the factor

1. **State the problem:** Behnaz has 6.3 kilograms of wax and uses it all to make candles. Each candle uses 210 grams of wax. She sells 2/5 of the candles at 13 each, then reduces

1. **State the problem:** Calculate the value of $$81^{\frac{3}{4}} \times 9^{\frac{1}{2}}$$. 2. **Recall the rules:**

1. The problem asks to find \textit{three quarters} of 1200. 2. To express \textit{three quarters} mathematically, we use the fraction $\frac{3}{4}$.

1. The problem is to provide a sample math problem with a detailed solution. 2. Let's consider a simple algebra problem: Solve for $x$ in the equation $$2x + 3 = 11$$.

1. **State the problem** Factor the expression $9u^2-30uv+25v^2$.

1. State the problem: Factor the expression $4x^2 + 36xw + 81w^2$. 2. Notice it is a perfect-square trinomial of the form $a^2 + 2ab + b^2$.

1. State the problem. Simplify $\left( 6x^2 y^3 + x^3 - 5x^3 y^2 \right) - \left( 2x^3 y^2 - 7y^2 + 4x^3 \right)$.

1. **State the problem** Solve the inequality for $y$: $$10-\frac{5}{8}y>15$$

## Problem: Classify each system and describe its solution For each system of linear equations, compare the two lines.

1. **State the problem:** Find the point of intersection of the two lines given by the equations: $$y = 10x - 6$$

1. The problem is about understanding where to place points on a plot and how to make them meet, which usually involves finding intersections or common points. 2. To find where two

1. **State the problem:** We need to graph the line given by the equation $$y - 4 = -\frac{2}{3}(x - 1)$$ which is in point-slope form. 2. **Recall the formula:** The point-slope f