🧮 algebra

1. The problem is to simplify the expression or solve the given algebraic problem in a shorter form. 2. To do this, identify the key operations such as addition, subtraction, multi

1. **State the problem:** Calculate the value of $6^2 - 4^2$. 2. **Recall the formula:** The expression is a difference of squares, which can be factored using the identity:

1. O problema pede para resolver o valor de $b$ passo a passo. 2. Para resolver $b$, precisamos de uma equação ou contexto que envolva $b$. Por favor, forneça a equação ou mais det

1. We are given two expressions to simplify and evaluate. 2. For the first expression, $x = \frac{1}{4} + \frac{1}{8} + \frac{3}{2}$.

1. **State the problem:** Solve the equation $$\frac{x-1}{x} - \frac{1}{5} = \frac{3x-3}{5x}$$ for $x$. 2. **Understand the equation:** We have fractions with variables in denomina

1. **State the problem:** Solve the quadratic equation $$3x^2 + 21x = 0$$ by factoring. 2. **Formula and rules:** To solve by factoring, first factor out the greatest common factor

1. **Problem 7:** Find which graph represents the system: $$2x + y = -4$$

1. **State the problem:** We are given the quadratic equation $x^2 = 9x - 20$ and asked to rewrite it in factored form and find the solution set. 2. **Rewrite the equation:** Move

1. **State the problem:** Solve the quadratic equation $$x^2 + 8x + 12 = 0$$ by factoring. 2. **Recall the factoring method:** To factor a quadratic $$ax^2 + bx + c = 0$$, find two

1. **State the problem:** Solve the quadratic equation $$x^2 + 13x + 42 = 0$$ by factoring. 2. **Recall the factoring formula:** For a quadratic equation $$ax^2 + bx + c = 0$$, we

1. **State the problem:** Solve the inequality $$\frac{x+1}{x(x+1)} \geq 2$$. 2. **Rewrite the inequality:** The expression can be simplified by noting the denominator is $x(x+1)$

1. **Problem Statement:** We start with 100 liters of water and 5 kilograms of sugar in a tank. Water is added at 10 liters per minute and sugar at 2 kilograms per minute. We want

1. **State the problem:** We have two function models: a linear function $L(x) = ax + b$ and a constant function $K(x) = a$. We are given predicted values for each at $x = 2.5$. 2.

1. **State the problem:** We are given the determinant of a 3x3 matrix:

1. **State the problem:** Simplify the algebraic expression $62xy + 17xy + 64 + xy - 18xyz + 21$. 2. **Identify like terms:** Like terms are terms that have the same variables rais

1. **Problem Statement:** Show that the determinant of the matrix $$\begin{vmatrix} a+b+2c & ab & c \\ b+c+2a & b & c \\ a & c+a+2b & b \end{vmatrix} = 2(a+b+c)^3.$$

1. **State the problem:** Simplify the algebraic expression $62xy + 17xyz + 64 + xy - 18xyz + 21$. 2. **Identify like terms:** Terms with the same variables and powers can be combi

1. **Stating the problem:** Simplify the given algebraic expressions by combining like terms. 2. **Recall the rules:**

1. **State the problem:** Simplify the expression $16 + 8d + 9e - 82 + 7de + 5 - d$. 2. **Group like terms:** Combine constants, terms with $d$, terms with $e$, and terms with $de$

1. **State the problem:** Simplify the expression $5p + 7q + 10 + 15p - 7q + 8t - 3$. 2. **Combine like terms:** Group terms with the same variables and constants.

1. **State the problem:** We need to solve and graph the inequality $$|u + 2| \geq 2$$ on the number line. 2. **Recall the rule for absolute value inequalities:** For any expressio