🧮 algebra

1. **State the problem:** Solve for $x$ in the equation $2(x-3)+3(x+1)=4(x-2)$.\n\n2. **Write down the equation:** $$2(x-3)+3(x+1)=4(x-2)$$\n\n3. **Distribute the constants:** Mult

1. **Solve the equation** $\frac{x - 6}{4x} = \frac{1}{2}$. 2. Multiply both sides by $4x$ to eliminate the denominator:

1. **State the problem:** Simplify the expression $$(2\sqrt{3} - 5)(2\sqrt{3} + 5)$$. 2. **Formula used:** This is a product of conjugates, which follows the difference of squares

1. El problema nos pide evaluar las funciones $f(x) = 4x^2 - x$ y $g(x) = -4x + 2$ en valores específicos: $f(-2)$ y $g(5)$. 2. Para evaluar una función en un valor dado, sustituim

1. The problem is to find the value of $X$. 2. Since no equation or context is given, we cannot solve for $X$ directly.

1. **State the problem:** Solve for $X$ in the equation:

1. **State the problem:** Simplify the expression $$(4-\sqrt{10})(4+\sqrt{10})$$. 2. **Formula used:** This is a product of conjugates, which follows the formula $$(a-b)(a+b) = a^2

1. Stating the problem: Simplify the expression $x^2y^2 - 5x^2y - 5xy^2 + xy$. 2. Group terms to factor by grouping:

1. The problem is to simplify the expression $$(\sqrt{5}+3)(\sqrt{5}-3)$$. 2. This is a product of conjugates, which follows the formula $$(a+b)(a-b) = a^2 - b^2$$.

1. The problem asks: What percent of 70 is 3.5? 2. To find what percent one number is of another, use the formula:

1. **State the problem:** Factor the expression $$x^2y^2 - 5x^2y - 5xy^2 + xy^3$$. 2. **Recall the factoring technique:** Group terms to factor by grouping.

1. **State the problem:** Simplify the expression $x^2y^2 - 5x^2y - 5xy^2 + xy^3$. 2. **Identify common factors:** Group terms to factor by grouping:

1. Diketahui fungsi $f(x) = x + 3$. Kita diminta mencari fungsi inversnya, yaitu fungsi $f^{-1}(x)$ yang memenuhi $f(f^{-1}(x)) = x$. 2. Langkah pertama, ganti $f(x)$ dengan $y$, s

1. The problem asks: How many 35ths are equal to $\frac{4}{7}$? 2. We want to find a number $x$ such that $\frac{x}{35} = \frac{4}{7}$.

1. **State the problem:** Find which of the given lines are tangent to the circle defined by the equation $$(x - 2)^2 + (y + 5)^2 = 20.$$ 2. **Recall the formula for tangency:** A

1. The problem is to find the slope of the linear function given by the equation $y = -5x - 1$. 2. Recall that the slope-intercept form of a line is $y = mx + b$, where $m$ is the

1. **State the problem:** Simplify the algebraic expression $2m + 3m + 5x + 6pt + 3m + 2p + 6x$. 2. **Identify like terms:** Like terms have the same variables raised to the same p

1. **State the problem:** Simplify the expression $$\frac{(2x^{-3}y^{-2})^{-2} (5x^{-4}y^{2})^{2}}{(10x^{2}y^{-5})^{1}}$$. 2. **Recall the exponent rules:**

1. The problem is to simplify the expression given by the user. 2. Since the user did not provide a specific expression, I cannot proceed with simplification.

1. **Problem Statement:** Solve the quadratic inequality $x^2 - 5x + 6 < 0$. 2. **Formula and Rules:** To solve a quadratic inequality, first find the roots of the corresponding qu

1. **State the problem:** We want to find how much sugar is needed to make 10 dozen cookies if 2 dozen cookies require 1 \frac{1}{3} cups of sugar. 2. **Convert mixed number to imp