🧮 algebra

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. We use the basic algebraic principle of isolating the variable $x$ by performing inverse operations.

1. **State the problem:** Simplify the expression $3x + 5x - 2x$. 2. **Recall the rule:** When simplifying algebraic expressions, combine like terms by adding or subtracting their

1. The problem is to evaluate the expression $0.9 \sqrt{0.51}$. 2. Recall that the square root function $\sqrt{x}$ gives the positive number which, when squared, equals $x$.

1. **State the problem:** Simplify the expression $-8 + (-x) - 3 + 7x$. 2. **Identify like terms:** Group the constant terms and the terms with $x$ separately.

1. **State the problem:** Factor the expression $$-8b^2 - 36b$$ completely. 2. **Identify the greatest common factor (GCF):** Both terms have a factor of $$-4b$$ because:

1. El problema pide simplificar la fracción $$\frac{6x - 24}{x^2 - 16}$$. 2. Primero, factorizamos el numerador y denominador por separado.

1. **Problem statement:** Find the cubic polynomial $P(x)$ with real coefficients that has zeros at $-3$, $-1$, and $4$, and a leading coefficient of $6$. 2. **Formula and rules:**

1. **State the problem:** Factor the expression $$5m^5 - 35m^2$$. 2. **Identify the greatest common factor (GCF):** Both terms have a factor of $$5m^2$$ because $$5$$ is common and

1. **State the problem:** Factor the polynomial $$7x^3 + 20x^2 - 3x$$. 2. **Identify common factors:** Notice that each term contains an $$x$$, so factor out $$x$$ first:

1. **State the problem:** Factor the polynomial $x^3 - 36x$ into linear factors. 2. **Identify the formula and rules:** To factor a polynomial, first look for a greatest common fac

1. **State the problem:** Determine if the equation $9x - (9x)^2 = 19 - y$ defines $y$ as a function of $x$. 2. **Rewrite the equation to express $y$ explicitly:**

1. The problem is to determine whether a given function is linear or nonlinear. 2. A function is linear if it can be written in the form $$y = mx + b$$ where $m$ and $b$ are consta

1. The problem asks: Which equation can you use to find $c$, the cost of each teacup? 2. We are given four equations:

1. El problema es hacer un análisis detallado y graficar la función dada. Sin embargo, no se especificó la función, así que tomaré un ejemplo común para explicar el proceso: la fun

1. **State the problem:** Determine if the function $x + (\sqrt{2}x)^2 + y - 2x^2 = 11$ is linear or nonlinear. 2. **Recall the definition of linear functions:** A function is line

1. **Problem Statement:** We have two rational numbers $a$ and $b$ on a number line, where $a < 0 < b$. The number $c$ is defined as the sum $c = a + b$. We need to determine which

1. **State the problem:** We need to order the expressions $2 - (-10)$, $-2 - 5$, $2 + (-10)$, and $-2 + 5$ from least to greatest. 2. **Recall rules for addition and subtraction o

1. **Stating the problem:** Solve the system of inequalities: $$2x + 3y > 8$$

1. The problem asks to find the "c.d of A.p" for the numbers 3, 4, 9, and 4-8. 2. First, clarify the terms: "A.p" likely means Arithmetic Progression (AP), and "c.d" means common d

1. **State the problem:** Divide the polynomial $4x^2 + 19x + 13$ by the binomial $x + 4$. 2. **Formula and rules:** Polynomial division can be done using long division or syntheti

1. The problem is to find the 8th term of the arithmetic progression (A.P.) with the first three terms given as $-3, -1, 1$. 2. Recall the formula for the $n$th term of an A.P.: