🧮 algebra

1. **State the problem:** Solve the equation $$\frac{8x}{5} - \frac{x}{4} = -3$$ for $x$. 2. **Find a common denominator:** The denominators are 5 and 4. The least common denominat

1. **State the problem:** Solve the equation $T - \frac{2}{5} = \frac{3}{2}$ for $T$. 2. **Isolate $T$:** To solve for $T$, add $\frac{2}{5}$ to both sides of the equation:

1. **State the problem:** Calculate the value of the expression $$[(-7)^2 - (-2)^6]^2$$.

1. Problema: Suma de polinomios Suma: $ (3x^4 + 5x^3 - 3x^2 + 25x - 2) + (4x^3 - 2x^2 + 1) $

1. Problema: Si 40 obreros hacen 100 m de carretera por día, ¿cuántos metros por día harán 70 obreros? 2. Fórmula: La regla de tres simple directa se usa cuando la relación entre d

1. The problem is to simplify $\sqrt{-18}$ into simplest radical form. 2. Recall that $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ and $\sqrt{-1} = i$ where $i$ is the imaginary

1. The problem is to simplify the radical expression $\sqrt{-10}$.\n\n2. Recall that the square root of a negative number involves the imaginary unit $i$, where $i = \sqrt{-1}$.\n\

1. **State the problem:** Determine if the given table of values satisfies a linear equation. 2. **Recall the formula for a linear equation:** A linear equation in two variables $x

1. **State the problem:** We are given a table of values for $x$ and $y$ and need to determine if these values satisfy a linear equation of the form $$y = mx + b$$ where $m$ is the

1. **State the problem:** Expand the expression $3(cd-4)(cd+4)$. 2. **Recall the formula:** Use the difference of squares formula: $ (a-b)(a+b) = a^2 - b^2 $. Here, $a = cd$ and $b

1. The problem is to simplify the expression $\frac{x}{x}$.\n\n2. The formula used here is the property of division: $\frac{a}{a} = 1$ for any $a \neq 0$. This means any nonzero nu

1. **State the problem:** Solve the equation $$4\sqrt{x} + 3 = 6\sqrt{x} - 2$$ for $x$. 2. **Isolate the square root term:** Move all terms involving $\sqrt{x}$ to one side and con

1. **State the problem:** Simplify and analyze the expression $x^3 - x$. 2. **Formula and rules:** To simplify, factor the expression by finding common factors.

1. The problem is to express $8c^2 - 2b^2$ as a difference of two squares. 2. Recall the difference of squares formula: $$a^2 - b^2 = (a - b)(a + b)$$

1. **State the problem:** Find the slope of the line segment JK where J(-1,-9) and K(5,3). 2. **Formula for slope:** The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is

1. **State the problem:** Solve the equation $2x:5 - x:3 = 4$. 2. **Rewrite the problem with clearer notation:** The colon ":" here represents division, so the equation is $\frac{2

1. The problem is to simplify or understand the expression $8c^2 - 2b^@$. 2. Notice that the expression contains an invalid character '@' which is not a standard mathematical symbo

1. **State the problem:** Factor the quadratic expression $x^2 + 5x + 6$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multipl

1. **State the problem:** Simplify the expression $ab^2 - a^3$. 2. **Identify common factors:** Both terms have a common factor of $a$.

1. **State the problem:** Simplify or factor the expression $a^2b^2 - c^2$. 2. **Recall the formula:** This expression is a difference of squares, which follows the rule:

1. **State the problem:** Simplify the expression $1 - a^2$. 2. **Recall the formula:** The expression $1 - a^2$ is a difference of squares, which can be factored using the identit