🧮 algebra

1. **Problem (i): Solve the equation** $$2^{2x-1} - 9 \cdot 2^{x-2} + 1 = 0$$ 2. **Rewrite terms using properties of exponents:**

1. **Problem:** Löse das Gleichungssystem mittels Additionsverfahren: $$\begin{cases} 2e - f = 9 \\ e + 3f = -6 \end{cases}$$

1. The problem is to understand and classify different types of real numbers. 2. Real numbers include rational numbers (which can be expressed as a fraction $\frac{p}{q}$ where $p$

1. **State the problem:** Compare the fractions $1 \frac{1}{2}$, $\frac{3}{2}$, and $\frac{17}{6}$ using $<$, $>$, or $=$. 2. **Convert mixed fractions to improper fractions:**

1. **State the problem:** We are given two equations: $$2x + 3y = 7$$

1. **State the problem:** Simplify the expression $$\frac{x^2-25}{x^2+5x} \div \frac{xy+6x-5y-30}{5x-15}$$. 2. **Rewrite the division as multiplication by the reciprocal:**

1. **State the problem:** Factor the quadratic expression $x^2 + 5x + 6$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multipl

1. **State the problem:** Solve the system of linear equations for $x$ and $y$: $$2x + y = 8$$

1. **State the problem:** We need to find values of $x$ and $y$ such that $$3^x - 3^y = 234.$$ 2. **Rewrite the equation:** We can factor the left side using the property of expone

1. **State the problem:** We need to solve the equation $$3^x - 3^y = 234$$ for the variables $x$ and $y$. 2. **Analyze the equation:** The equation involves exponential terms with

1. The problem is to evaluate the expression $6 \div 2(1+2)$.\n\n2. According to the order of operations (PEMDAS/BODMAS), first solve the parentheses.\n\n3. Calculate inside the pa

1. The problem is to evaluate the expression $6 \div 2(1+2)$. 2. According to the order of operations (PEMDAS/BODMAS), we first solve expressions inside parentheses.

1. Let's solve an example logarithm problem: Find $x$ if $\log_2(x) = 3$. 2. The logarithm formula states that $\log_b(a) = c$ means $b^c = a$.

1. Let's start by stating the problem: factoring a function means expressing it as a product of simpler functions or polynomials. 2. The most common type of factoring is factoring

1. The problem is to simplify the expression $x^2 + x^2$. 2. The formula used here is the addition of like terms: $a^n + a^n = 2a^n$.

1. **State the problem:** Solve the equation $16 - 2t = 5t + 9$ for $t$. 2. **Write down the equation:**

1. **State the problem:** We are given three equations involving apple, banana bunch, and coconut half: - apple + banana bunch + banana bunch = 18

1. **State the problem:** Simplify the expression $6 \div 2(1+2)$. 2. **Evaluate inside the parentheses first:** $1+2=3$. So the expression becomes $6 \div 2(3)$.

1. **State the problem:** We have a total of $p=342$ peanuts divided equally into 6 bags. We want to find how many peanuts are in each bag. 2. **Identify the operation:** Since the

1. The problem asks which scenario corresponds to the algebraic expression $\frac{365}{y}$. 2. The expression $\frac{365}{y}$ means "365 divided by $y$."

1. Let's clarify how we get the number 6 in the context of a problem. 2. Suppose the problem involves solving an equation or simplifying an expression that results in 6.