🧮 algebra

1. **State the problem:** Solve for $x$ in the equation $-\frac{1}{2} = \frac{4}{9}x + \frac{5}{6}$. 2. **Isolate the term with $x$:** Subtract $\frac{5}{6}$ from both sides:

1. **State the problem:** Solve for $y$ in the equation $$-\frac{1}{4} = -\frac{1}{4} + \frac{1}{8}y.$$\n\n2. **Isolate the term with $y$:** Add $\frac{1}{4}$ to both sides to elim

1. Das Problem lautet: Schreibe $[(-3)^7]^3$ als Potenz in der Form $a^b$. 2. Die Potenzregel für Potenzen lautet: $$(a^m)^n = a^{m \cdot n}$$

1. Das Problem lautet: Berechne den Wert von $$[(-3)^7]^3$$. 2. Die Potenzregel für Potenzen besagt: $$ (a^m)^n = a^{m \cdot n} $$.

1. **State the problem:** Calculate the gross pay for the week given the work schedule and hourly pay rate of 16.50 per hour. 2. **Identify work hours:**

1. The problem is to understand the difference between the variables $5$ and $s$. 2. In algebra, $5$ is a constant number, while $s$ is a variable that can represent any number.

1. **State the problem:** Simplify the expression $$\frac{C^{5+4}}{C^2 \cdot C^{1-5}}$$. 2. **Use the laws of exponents:** When dividing powers with the same base, subtract the exp

1. The problem is to understand if the expression "5:12" is in ratio form. 2. A ratio compares two quantities and is written as $a:b$ where $a$ and $b$ are numbers.

1. **State the problem:** Solve for $t$ in the proportion $$\frac{2}{5} = \frac{30}{3t + 9}.$$\n\n2. **Use the cross-multiplication rule for proportions:** If $$\frac{a}{b} = \frac

1. **State the problem:** Find the solutions of the quadratic equation $$5x^2 - 2x - 9 = 0$$ where $$x \in \mathbb{R}$$, correct to 2 decimal places. 2. **Recall the quadratic form

1. The problem states that there are 12 blue triangles for every 27 yellow triangles. 2. We are asked to find the ratio of yellow triangles to blue triangles.

1. **State the problem:** Solve for $q$ in the equation $$\frac{q + 2}{5} = \frac{2q - 11}{7}.$$\n\n2. **Formula and rules:** To solve an equation with fractions, we can eliminate

1. **State the problem:** We are given the proportion $$\frac{45}{35} = \frac{9}{7a - 7}$$ and need to find the value of $a$. 2. **Recall the property of proportions:** If $$\frac{

1. **State the problem:** Simplify the expression $\frac{X}{2x^2 - 1}$. 2. **Identify the expression:** The numerator is $X$ and the denominator is $2x^2 - 1$.

1. We are asked to find the value of the function $F$ at $x = -\frac{1}{2}$. However, the function $F(x)$ is not given in the problem statement. 2. To evaluate $F\left(-\frac{1}{2}

1. **State the problem:** Simplify the expression $$\left(\frac{5}{6}\right)^2 \times (-36) + \frac{5}{7} \div \left(-\frac{25}{14}\right)$$. 2. **Recall the rules:**

1. **Problem:** Wandle den Term (−x + 3y)² mithilfe der binomischen Formeln in eine Summe um. 2. **Formel:** Die zweite binomische Formel lautet $$ (a - b)^2 = a^2 - 2ab + b^2 $$

1. **State the problem:** Simplify the expression $$\frac{ab^5 c^0}{a^0 b^{-1} c \cdot a^9 b^{-1} c}$$. 2. **Recall exponent rules:**

1. **State the problem:** Solve the inequality $$\ln(x-2) + \ln\left(\frac{x}{3}\right) \le 0$$ for $x$. 2. **Use logarithm properties:** Recall that $$\ln(a) + \ln(b) = \ln(ab)$$

1. **State the problem:** Simplify the expression $$bc^2 \cdot b^0 c^{-3} \cdot b^{-2} c$$ and express the answer using positive exponents. 2. **Recall exponent rules:**

1. The problem asks to identify two equations that represent the relationship between $x$ (camel rides) and $y$ (elephant rides). 2. The first type of equation is a linear equation