🧮 algebra

1. The problem asks to expand the expression $2\log_4(X+4)$.\n\n2. Recall the logarithm power rule: $a\log_b(c) = \log_b(c^a)$. This means we can rewrite the coefficient 2 as an ex

1. The problem is to simplify the fraction $\frac{3}{6}$. 2. The formula to simplify a fraction is to divide the numerator and denominator by their greatest common divisor (GCD).

1. Problem: Reduce the fraction $\frac{2}{4}$ to its lowest terms. 2. Formula: To reduce a fraction to its lowest terms, divide the numerator and denominator by their greatest comm

1. **Problem Statement:** Prove that the product $n(n+1)(n+2)$ is divisible by 3 for all integers $n > 1$ using the principle of mathematical induction. 2. **Induction Principle:**

1. The problem is to solve the inequality $\frac{m}{5} \geq 7$. 2. To isolate $m$, multiply both sides of the inequality by 5. Since 5 is positive, the inequality direction remains

1. **State the problem:** Simplify the expression $$\frac{\left(\frac{1}{2}\right)^x \cdot 8^x}{4^x}$$. 2. **Recall the laws of exponents:**

1. Masalah: Jumlah umur kakak dan dua kali umur adik adalah 27 tahun, dan selisih umur kakak dan adik adalah 3 tahun. Jika umur kakak adalah $x$ tahun dan umur adik adalah $y$ tahu

1. **State the problem:** Simplify the expression $$\frac{2a - 3b5'}{(2a - 1b)3}$$. 2. **Interpret the expression:** The numerator is $$2a - 3b5'$$ and the denominator is $$(2a - 1

1. **Stating the problem:** A quadratic equation is any equation that can be written in the form $$ax^2 + bx + c = 0$$ where $a$, $b$, and $c$ are constants and $a \neq 0$. 2. **Me

1. **State the problem:** The heights of two poles are in the ratio 9:5. The height of the shorter pole is 8 m. Find the height of the taller pole. 2. **Formula and rules:** If two

1. The problem asks to write inequality statements as mathematical expressions. 2. Inequality statements compare two values using symbols: greater than ($>$), less than ($<$), grea

1. **Problem 2:** The heights of 2 poles are in a ratio of 9:5. The height of the shorter pole is 8 m. What is the height of the taller pole? 2. **Set up the proportion:** Let the

1. **State the problem:** We need to find how many students at Pierrefonds Comprehensive High School are learning to play the guitar. 2. **Given information:**

1. **State the problem:** Multiply the fractions $\frac{7}{8}$ and $\frac{6}{1}$. 2. **Formula used:** To multiply fractions, multiply the numerators together and the denominators

1. **State the problem:** Solve the equation $x - y = 11$ for one variable in terms of the other. 2. **Formula and rules:** This is a linear equation in two variables. To express o

1. **State the problem:** Solve the equation $x - y = 11$ for one variable in terms of the other. 2. **Formula and rules:** This is a linear equation in two variables. To express o

1. **State the problem:** Simplify the expression $-(5f+2)+5f$. 2. **Apply the distributive property:** The negative sign before the parentheses means we multiply each term inside

1. **State the problem:** Simplify the expression $$\frac{2}{x-3} + \frac{3}{x+2} - \frac{4x-7}{x^2 - x - 6}$$. 2. **Identify the denominator factorization:** The quadratic in the

1. **State the problem:** Simplify the expression $$\frac{2}{x-3} + \frac{3}{x+2}$$. 2. **Formula and rules:** To add rational expressions, find a common denominator, which is the

1. **State the problem:** Simplify the expression $$\frac{4a^2-(x-3)^2}{(2a+x)^2-9}$$. 2. **Recall formulas:** This expression involves differences of squares. Recall that $$A^2 -

1. **State the problem:** Simplify the expression $$(2a + x)^2 - 9$$. 2. **Recall the formula:** The square of a binomial is given by $$(A + B)^2 = A^2 + 2AB + B^2$$.