🧮 algebra

1. Problem statement: Simplify the expression $$-3 - [4x + 7x - (12 + 2x) + 4]$$ for $$x = -2$$. 2. Combine like terms inside the brackets:

1. Problem: Löse die Gleichung a) $7 \cdot 5^x = 9 - 6 \cdot 5^x$. 2. Wir wollen $x$ finden, das die Gleichung erfüllt.

1. **State the problem:** Factorise the expression $6x - 4$. 2. **Recall the factoring rule:** To factorise an expression, find the greatest common factor (GCF) of all terms.

1. **State the problem:** Fully factorise the expression $8p + 12$. 2. **Identify the common factor:** Both terms $8p$ and $12$ have a common factor of $4$.

1. **State the problem:** Solve the equation $$9^{3x - 7} = 81^{x + 2}$$. 2. **Rewrite bases as powers of the same base:**

1. **State the problem:** Solve the exponential equation $$2e^{5x} = 868$$ by taking the natural logarithm on both sides. 2. **Isolate the exponential term:** Divide both sides by

1. **State the problem:** Calculate the gross pay for the week given hourly wage, hours worked, and tips. 2. **Formula:** Gross pay = (hourly wage × hours worked) + (percentage of

1. **State the problem:** Calculate the gross pay for the week if you are paid 16.50 per hour and work the following hours: - Monday: 5:00 PM to 10:00 PM

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{