🧮 algebra

1. Problem: Find the solution set for \(|x-5| \leq 4\). Step 1: Recall that \(|x-a| \leq b\) means \(a-b \leq x \leq a+b\).

1. The problem states that a human blinks approximately $8 \times 10^{6}$ times in 1 year. 2. We need to find the total blinks in 3 years, so we'll multiply the yearly blinks by 3.

1. The problem describes a number line with points A, 4, and B in that order. There is a green arrow labeled "+5" pointing from A to 4 and a purple arrow labeled "+8" pointing from

1. **Calculer A et B** Calcul de A:

### Exercice 1 1. Calculer:

1. Factor the expression $abx^3 + (a - 2b - ab)x^2 + (2b - a - 2)x + 2$ fully. Step 1: Group terms:

1. Stating the problem: Solve the equation $$-2 \log_{5}(x) = \log_{5}(121)$$ for $x$. 2. Use the logarithm power rule on the left side: $$-2 \log_{5}(x) = \log_{5}(x^{-2})$$.

1. **State the problem:** Solve the equation $$\log_8(-4x + 194) = \log_8(13x - 10)$$ for $x$. 2. **Apply the property of logarithms:** Since the logarithms on both sides have the

1. Énonçons le problème: résoudre l'expression $$n^{2024} + 3 + \frac{(n+3)^{2025}}{2}$$ par disjonction de cas. 2. La disjonction de cas consiste à étudier séparément les cas où l

1. **State the problem:** Solve for $x$ in the equation $$8^{10x-9} = 2^{7x-4}$$. 2. **Rewrite the bases as powers of 2:**

1. The user's question "With x^?" is unclear, but it suggests a query about expressions involving powers of $x$. 2. Let's explain how to interpret and work with expressions like $x

1. We are given the equation $$e^{7x} = 14$$ and need to solve for $$x$$. 2. Recall that the natural logarithm $$\ln$$ is the inverse function of the exponential function with base

1. The problem is to find the value of $3^9 - 3^8$. 2. Recall that $3^9 = 3^{8+1} = 3^8 \cdot 3^1$.

1. The problem is to solve the exponential equation $$4^{-8w - 15w^2} = 4.$$ 2. Rewrite the right side as a power of 4: $$4 = 4^1.$$ So the equation becomes $$4^{-8w - 15w^2} = 4^1

1. State the problem: Evaluate $\left(\sqrt{4} + 3i\right)^5$. 2. Simplify inside the parenthesis: $\sqrt{4} = 2$, so the expression becomes $\left(2 + 3i\right)^5$.

1. **Problem statement:** Solve the system of linear equations using Gauss Elimination method: $$\begin{cases} 2x_1 + 2x_2 + x_3 = 6 \\ 4x_1 + 2x_2 + 3x_3 = 4 \\ x_1 + x_2 + x_3 =

1. The problem is to evaluate the expression $\sqrt{4 + 3i}$. 2. To find the square root of a complex number, we assume it can be written as $a + bi$ where $a$ and $b$ are real num

1. **State the problem:** We are given the black curve with equation $y = x^3 + 2x^2 + 1$.

1. The problem gives the black curve with equation $$y = x^3 + 2x^2 + 1$$ and asks for the equation and transformation of the red curve relative to the black curve. 2. Observing th

1. **State the problems:** We have several systems and inequalities to analyze and solve. ---

1. The problem involves simplifying and understanding the expression: $$\frac{2(y=om)^2T}{8} + \frac{(106s)^2T}{8} + \left( \sin^2 7 7 8 \right)^2 - 2 \sin^2 7 7 8 \cos^2 7 7 8 + \