🧮 algebra

1. **State the problem:** Expand the expression $$6a (5a - 8b - 1)$$. 2. **Formula used:** To expand, use the distributive property: $$x(y + z + w) = xy + xz + xw$$.

1. Намерете x, ако: а) $2^5 = x$

1. **State the problem:** Find the first three terms of the sequence defined by the nth term formula $a_n = 3n + 1$. 2. **Formula used:** The nth term of the sequence is given by $

1. **Problem statement:** Solve the equation $$x^2 = |2x + 4| + |x - 2|$$ for real values of $x$. 2. **Key idea:** Because of the absolute values, split the problem into intervals

1. **State the problem:** Solve the equation $8k - 19 = 3 + 16$ for $k$. 2. **Simplify the right side:**

1. **State the problem:** We need to find the numbers that go in the two red square boxes in the equation: $$2(\square - 4x) + \square(3x - 1) = 2(2x + 3)$$

1. **Problem statement:** Calculate the total net salary paid by company "A" in December based on the given employee data. 2. **Given data:**

1. **State the problem:** Solve the system of equations for $x$, $y$, and $z$: $$\begin{cases} x + y + 2x = 4 \\ x + y + 3x = 5 \\ 2x + y + z = 2 \end{cases}$$

1. **State the problem:** Solve the system of equations: $$\begin{cases} x + y + 2x = 4 \\ x + y + 3x = 5 \\ 2x + y + z = 2 \end{cases}$$

1. Problem: Solve the equation $$|x+4| + |3x+3| = |x| + 10$$ and verify the solution. 2. Identify critical points where expressions inside absolute values change sign:

1. Bài toán yêu cầu tính giá trị của định thức $$\Delta=\begin{vmatrix}0 & 2 & 0 \\ m & 0 & -1 \\ 0 & m+1 & 2 \\ 3 & -m & -2 \\ -m & m+1 & 1 \\ m & -1 & 0\end{vmatrix}$$ với tham s

1. **State the problem:** Solve the equation $x + 2 = 6$ for $x$. 2. **Formula and rules:** To isolate $x$, subtract 2 from both sides of the equation. This uses the subtraction pr

1. **State the problem:** Simplify the expression $x + 2(8 + 2)$. 2. **Apply the order of operations:** First, solve inside the parentheses.

1. **Problem:** Fully factorise the quadratic expression $2x^2 + 12x + 18$. 2. **Formula and rules:** To factorise a quadratic expression of the form $ax^2 + bx + c$, first look fo

1. Muammo: Berilgan arifmetik progressiya hadlari $\{a_n\}$ va geometrik progressiya hadlari $\{b_n\}$ uchun shartlar berilgan: $b_1 + b_2 + b_3 = 65$, $b_6 > b_5$, $b_1 - a_1 = 1$

1. **Problem statement:** We have two sequences: an arithmetic progression $\{a_n\}$ and a geometric progression $\{b_n\}$. Given: - $b_1 + b_2 + b_3 = 65$

1. **State the problem:** Find the 5th term of the sequence defined by $T_n = 3n - 2$. 2. **Formula:** The general term of the sequence is given by $T_n = 3n - 2$.

1. **State the problem:** Solve the equation $\frac{26991.5}{x} = 0.025$ for $x$. 2. **Formula and rules:** To solve for $x$ when it is in the denominator, multiply both sides of t

1. **State the problem:** Solve for $x$ in the equation $\frac{25991.5}{x} = 0.025$. 2. **Formula and rules:** To solve for $x$ when it is in the denominator, multiply both sides b

1. **பிரச்சினை:** பொதுஉறுப்பு $T_n = 3n - 2$ எனில், அதன் 5 ஆம் உறுப்பை காண்க. 2. **பொருள்:** பொதுஉறுப்பின் சூத்திரம் $T_n = 3n - 2$.

1. **Nyatakan masalah:** Selesaikan persamaan $$2(k - 1) = -\frac{5}{2}$$. 2. **Gunakan formula dan peraturan:** Kita akan gunakan sifat pengagihan dan operasi algebra asas untuk m