🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{6x - 1}{3x - 4} + \frac{4x - 1}{4 - 3x}$$ given the restrictions $$x \neq 4$$ and $$x \neq -1$$. 2. **Identify the restric

1. **State the problem:** Solve the system of equations by graphing: $$2x + y = 2$$

1. **State the problem:** Solve the equation $7A = -2[-7 - 3(4) + 5 - 2(-1)] + 3(6 + 8)$. 2. **Apply the order of operations:** Start by simplifying inside the brackets and parenth

1. Stating the problem: Simplify the expression $$3 \left(\frac{11}{12} - \frac{5}{6}\right) + \frac{3}{4}$$. 2. Use the order of operations: first simplify inside the parentheses,

1. The problem asks to find the constant of proportionality for each proportional relationship given in the table and for the equation $y=1.3x$. 2. The constant of proportionality

1. **State the problem:** Simplify the expression $-5(6m + 3) - 7(-7m + 7)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside

1. **State the problem:** Simplify the expression $-4(8f + g) + 9g - 5(-2g + 6f)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor o

1. **Stating the problem:** We need to find the value of $x$ in an addition problem where the total was mistakenly taken as 540 instead of 431. 2. **Understanding the problem:** If

1. The problem involves evaluating the function $g(x)$ at specific points and understanding the range of $g$. 2. Part A states the range is $(-\infty, 4]$. This means $g(x)$ can ta

1. **State the problem:** Aurora baked some cookies. She gave 12 cookies to her family, sold \(\frac{7}{9}\) of the cookies at a bake sale, and had 8 cookies left over. We need to

1. The problem is to solve the inequality $$6x \geq 108$$ and find all possible values of $x$ that satisfy it. 2. The formula used here is to isolate $x$ by dividing both sides of

1. **State the problem:** We need to determine which values among I. 7.5, II. \frac{22}{3}, and III. 8 satisfy the inequality $$\frac{x}{3} > 2\frac{1}{2}$$. 2. **Rewrite the inequ

1. **State the problem:** Simplify and expand the expression $(x-2)^2$. 2. **Formula used:** The square of a binomial $(a-b)^2$ is given by $$ (a-b)^2 = a^2 - 2ab + b^2 $$

1. **State the problem:** Factor out the greatest common factor (GCF) from the polynomial $$5x^4 - 25x^3 + 10x^2$$. 2. **Identify the GCF:** Look at the coefficients 5, 25, and 10.

1. The problem is to factor the trinomial $x^2 - 12x - 45$ or determine if it is prime. 2. The general form of a quadratic trinomial is $ax^2 + bx + c$. Here, $a=1$, $b=-12$, and $

1. **State the problem:** Solve the system of equations by elimination: $$10x + 2y = 18$$

1. **Problema:** Resolver a inequação $$4^{-1} + 2x \leq \frac{1}{2} - 3x$$. 2. **Fórmula e regras:** Para resolver inequações, isolamos a variável $x$ em um lado da desigualdade,

1. **State the problem:** Simplify the complex fraction $$\frac{\frac{2}{x} + 7}{8}$$. 2. **Rewrite the numerator:** The numerator is $$\frac{2}{x} + 7$$. To combine these terms, w

1. **Problem statement:** We want to find the function term of a cubic polynomial $f(x)$ that models the curve profile of a swing lounger. The function is a cubic polynomial symmet

1. **Planteamiento del problema:** Simplificar la expresión $$\frac{x^2 - 2x - 3}{x^2 + x - 6} \div \frac{x - 3}{4x - 8}$$. 2. **Regla para dividir fracciones:** Dividir por una fr

1. **State the problem:** Evaluate the cube root of -81, i.e., find $\sqrt[3]{-81}$.