🧮 algebra

1. **State the problem:** Solve the equation $$a(x - 1) - \frac{1 - 2x^2}{2} = (x - 4)(4 + x) + 3(1 + a)$$ for $a$ when $x = -\frac{7}{2}$.\n\n2. **Substitute $x = -\frac{7}{2}$ in

1. **State the problem:** Solve the equation $$(x - 1)^3 + \frac{3}{2}(2x + 3)^2 + (-1 - x)^3 = 18x.$$\n\n2. **Rewrite the equation:** Note that $(-1 - x)^3 = -(x + 1)^3$. So the e

1. **Stating the problem:** Simplify the expression $$\frac{x^{\frac{2}{3}}}{x^{\frac{1}{3}}}$$ and express it in the form $$x^a$$. 2. **Formula used:** When dividing powers with t

1. **State the problem:** Solve the equation $$\frac{\left(2x - \frac{1}{3}\right)(3 - x)}{5} + \frac{(2x + 1)^2}{10} + \left(\frac{1}{10} - \frac{1}{5}\right)^{-1} \left(\frac{x}{

1. **State the problem:** Solve the equation $$1.1 \times 10^{-12} - 2x^3 - 0.2x^2 = 0$$ for $x$. 2. **Rewrite the equation:** Move all terms except the constant to the right side:

1. **State the problem:** Solve the equation $$\frac{7}{12}x + \frac{10x - 15}{3} - x = \frac{4(2x - 1)}{3} - \frac{3(2 - x)}{4}$$ for $x$. 2. **Identify the goal:** We want to iso

1. Let's solve the first algebraic expression: $x + 142 = 16x + 7$. 2. The goal is to isolate $x$ on one side. Start by moving all $x$ terms to one side and constants to the other:

1. **State the problem:** Solve the equation $1.1 \times 10^{-12} = 2x^2(x + 0.1)$ for $x$. 2. **Rewrite the equation:**

1. **State the problem:** Solve the equation $$-\frac{(2-3y)^2}{54} = 0.666\ldots y + \frac{(y+0.5)(0.3333\ldots - y)}{6}$$ for $y$. 2. **Rewrite repeating decimals as fractions:**

1. **State the problem:** Simplify the expression $$7 - \frac{5^2 + 3}{(-1)^2}$$ using order of operations. 2. **Recall order of operations:** Parentheses, Exponents, Multiplicatio

1. **State the problem:** Simplify the expression $2 + 1^3 \times 10 - 3$ using the order of operations. 2. **Recall the order of operations:** Parentheses, Exponents, Multiplicati

1. Proporcionalidade Direta entre t e N: 1.1. Dado que $t$ e $N$ são diretamente proporcionais, temos a relação $N = k t$, onde $k$ é a constante de proporcionalidade.

1. **State the problem:** We are given the function $$y = \frac{4}{x} + \sqrt{x} + 0.2 - 5x$$ and the value $$x = \frac{4}{5}$$.

1. **State the problem:** Solve the equation $2x + 3 = 7$ for $x$. 2. **Use the formula:** To solve a linear equation of the form $ax + b = c$, isolate $x$ by subtracting $b$ from

1. **State the problem:** Evaluate the logarithmic expression $$\log_3 27 - \log_2 4$$. 2. **Recall the logarithm rules:**

1. **State the problem:** Simplify the expression $\log_{2025} 2025 - \log_3 \left( \frac{1}{9} \right)$.\n\n2. **Recall the logarithm properties:**\n- $\log_a a = 1$ for any base

1. We start with the first equation: $3x^{2} - 4 = 1(-x - 2)$. 2. Distribute the right side: $3x^{2} - 4 = -x - 2$.

1. **State the problem:** Solve for $x$ in the equation $$4.0 \times 10^{-11} = x(2x + 0.10)^2.$$\n\n2. **Rewrite the equation:** Note that $0,10$ is a comma decimal notation, so r

1. **Stating the problem:** We have several tables and number lines showing relationships between quantities and their percent values. The goal is to find missing values marked as

1. **State the problem:** Solve the equation $2x^3 + 0.10x = 4.0 \times 10^{-11}$ for $x$. 2. **Rewrite the equation:**

1. **State the problem:** We need to find the cost of two types of concert tickets: a cheaper ticket and a more expensive ticket that costs 30 more than the cheaper one. A group bu