🧮 algebra

1. El problema es simplificar la expresión \( (-2x^{2}y - 3x^{3} - 2y^{3} + 2xy^{2}) - (-3x - 4x^{2}y + yx - 5x^{2}y^{2} - 3y^{2}x) \). 2. Primero, eliminamos los paréntesis y camb

1. The problem is to solve the equation $x = x + 1$ for $x$. 2. Start by subtracting $x$ from both sides to isolate the constant term:

1. The problem asks to simplify the expression $w + w$. 2. Since both terms are the same variable $w$, we can combine them by addition.

1. **State the problem:** We are given a piecewise function: $$f(x) = \begin{cases} 3x + 5 & -4 \leq x \leq -1 \\ 2 & -1 \leq x < 3 \\ -x + 2 & 3 \leq x \leq 4 \end{cases}$$

1. **State the problem:** We have a piecewise function defined as: $$f(x) = \begin{cases} 3x + 5 & -4 \leq x \leq -1 \\ 2 & -1 \leq x < 3 \\ -x + 2 & 3 \leq x \leq 4 \end{cases}$$

1. The problem presents two expressions: $36 + 39$ and $23 - 3$, and also includes integral and partial derivative notation. 2. First, evaluate the simple arithmetic expressions:

1. The problem is to verify if the equation $36 + 34 = 36$ is true. 2. First, calculate the left side: $36 + 34 = 70$.

1. The problem asks to express the first answer in the form of the equation $py - m(x - a) = b$. 2. To do this, identify the variables and constants in the original answer and rear

1. **State the problem:** We need to find how many adult tickets were sold given that child tickets cost 5.50, adult tickets cost 9.30, a total of 121 tickets were sold, and the to

1. **State the problem:** We are given the linear function $y = 2x + 3$ and asked to find the value of $y$ when $x = 2$. 2. **Substitute the value of $x$ into the equation:** Repla

1. Stating the problem: Solve the equation $$\frac{2x-1}{4} - \frac{x+1}{12} = \frac{5x+3}{6}$$ for $x$. 2. Find the least common denominator (LCD) of 4, 12, and 6, which is 12.

1. **State the problem:** We are given the system of equations: $$x^2 - 2y^2 = 73$$

1. **State the problem:** Solve the inequality $$(3 - x)^2 < \frac{16}{25}$$. 2. **Rewrite the inequality:** Since the square of a real number is always non-negative, we can take t

1. Stating the problem: Solve the inequality $$(3 - x)^2 < \frac{16}{25}$$. 2. Take the square root on both sides, remembering to consider both positive and negative roots:

1. The problem asks: At midnight, how many degrees colder was Paris than Rome? 2. From the table, Paris at midnight is $-4$ degrees and Rome at midnight is $3$ degrees.

1. **State the problem:** We need to find the difference in the estimated lengths of two alligators. The length is estimated by measuring the distance from the eyes to the nose and

1. The problem asks us to find the common factors of both 12 and 18. 2. First, find the factors of 12: 1, 2, 3, 4, 6, 12.

1. **Convert numbers to standard form:** - $963000 = 9.63 \times 10^{5}$

1. **Match each calculation to its correct answer:** - Calculate $3 \times 10^3$:

1. **Simplify the expression** $3 + 2(5x - 6)$. Step 1: Apply the distributive property: $2 \times 5x = 10x$ and $2 \times (-6) = -12$.

1. The problem is to prove that an expression is equal to $$\frac{\sqrt{x+1} - \sqrt{x-1}}{\sqrt{2}}$$.\n\n2. Let's start by assuming the expression to prove is given or we want to