🧮 algebra

1. **State the problem:** We are given the equation $\log JC - \log (2x-1) = 1$ and need to find the value of $x$.

1. Problem: Simplify and understand the expression $\sqrt{y}$, which represents the square root of $y$. 2. Formula: The square root of a number $y$ is a value that, when multiplied

1. **State the problem:** Al earns a commission of 0.0125 (or 1.25%) on every dollar of the sales price. We need to find his commission on a $150,000 house. 2. **Formula:** Commiss

1. **Problem Statement:** Determine the number to add to each expression to make it a perfect square trinomial and then express it as a square of a binomial. 2. **Formula Used:** T

1. **Problem Statement:** Determine the number to add to each binomial to make it a perfect square trinomial, then express it as a square of a binomial. 2. **Formula:** To complete

1. **State the problem:** Simplify and rationalize the expression $$\sqrt{\frac{18}{2}}$$ assuming all variables represent positive numbers. 2. **Recall the property of square root

1. **State the problem:** Simplify the expression $2^{k+1} + 2^{k+1}$. 2. **Recall the rule for adding like terms with exponents:** When terms have the same base and exponent, you

1. **State the problem:** Simplify the expression $2^{k+1} + 2^{k+1}$. 2. **Recall the rule for adding like terms with exponents:** When the bases and exponents are the same, you c

1. **State the problem:** Simplify and understand the expressions involving $t$ and square roots, and evaluate the product $\sqrt{5} \times \sqrt{3} \times \sqrt{2}$.\n\n2. **Recal

1. The problem is to solve the equation labeled as "Ex 2". Since the user did not provide the explicit equation, I will assume a common example for "Ex 2" in algebra: solving a qua

1. **Stating the problem:** Simplify the expression $$\frac{3\sqrt{x} - 5}{2} \times 6\sqrt{x} - 5$$. 2. **Rewrite the expression clearly:** The expression is $$\left(\frac{3\sqrt{

1. **Énoncé du problème :** Résoudre le système linéaire suivant par la méthode de Cramer : $$\begin{cases} 2x + 3y - z = 4 \\ x + 2y + z = 3 \\ x + y + 2z = 5 \end{cases}$$

1. The problem is to solve the equation clearly, but since no specific equation is given, I will demonstrate solving a simple algebraic equation as an example: Solve for $x$ in $2x

1. **Problem:** Determine whether the system of equations is consistent or inconsistent, independent or dependent. Given system:

1. The problem is to evaluate the expression $\frac{1}{5}$.\n\n2. This is a simple fraction representing one part of five equal parts.\n\n3. The fraction $\frac{1}{5}$ can be conve

1. **State the problem:** Solve for $n$ in the equation $$24=3(n-5)$$. 2. **Use the distributive property:** Multiply 3 by each term inside the parentheses:

1. **State the problem:** Solve for $n$ in the equation $$7n - 4 = 31$$. 2. **Add 4 to both sides to isolate the term with $n$:**

1. დავიწყოთ პირველი შეკითხვით: გამარტივება \(\sqrt{\frac{0.64 \times 81}{49}}\).\n 2. გამოვიყენოთ წესი: \(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\) და \(\sqrt{a \times b} =

1. **State the problem:** Factorise the quadratic expression $x^2 + 5x - 14$. 2. **Recall the formula and rules:** To factorise a quadratic expression of the form $ax^2 + bx + c$,

1. Diketahui sebuah masalah matematika, kita mulai dengan menyatakan rumus yang digunakan dan apa yang ditanyakan. 2. Misalnya, jika masalahnya adalah mencari nilai $x$ dari persam

1. დავიწყოთ პირველი შეკითხვით: გამარტივება \(\sqrt{\frac{0.64 \cdot 81}{49}}\).\n\n2. გამოვიყენოთ წესი: \(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\) და \(\sqrt{a \cdot b} = \