🧮 algebra

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

1. **State the problem:** Simplify the expression $$\frac{7(2v + 3)(v + 7)}{28(v - 4)(2v + 3)}$$. 2. **Identify common factors:** Notice that both numerator and denominator contain

1. **State the problem:** Translate the sentence "Twice the difference of a number and 3 is 5" into an equation using the variable $w$ for the unknown number. 2. **Understand the k

1. **State the problem:** Simplify the expression $$\left(\frac{-7a}{b^{3}}\right)^2$$ without parentheses. 2. **Recall the rule:** When raising a fraction to a power, raise both n

1. **State the problem:** Factor the quadratic expression $$49w^2 + 42wv + 9v^2$$. 2. **Formula and rules:** This is a quadratic trinomial in two variables. We look for factors of

1. The problem is to rewrite the expression $\left(\frac{7}{5}\right)^{-1}$ without an exponent. 2. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$.

1. The problem asks to find the coordinates of point Z on the graph of the linear equation $$y = 0.8x - 3$$ when $$x = 2$$. 2. The formula for a linear function is $$y = mx + b$$,