🧮 algebra

1. **Problem 1: Calculate cost price and selling price with given profit percentages** 2. **Given:**

1. **Problem:** Solve $|2s - 7| \geq -1$. Since absolute value is always non-negative, $|2s - 7| \geq -1$ is always true for all real $s$.

1. **Stating the problem:** We will solve an example of simultaneous equations and a quadratic equation.

1. **Understanding Equations** An equation is a mathematical statement that asserts the equality of two expressions, typically containing variables.

1. **Problem 1:** Solve the quadratic inequality $$x^2 - 5x + 6 < 0$$ and express the solution in interval notation and set-builder notation. 2. **Problem 2:** Solve the quadratic

1. **State the problem:** We want to learn how to solve equations, which means finding the value(s) of the variable(s) that make the equation true. 2. **Formula and rules:** An equ

1. **State the problem:** Find the domain of the function $$y = \frac{\sqrt{6x^2 + 11x - 7}}{\sqrt{|2x - 5| + 4x^2 - 2x - 13}}$$. 2. **Recall domain rules for such functions:**

1. **Problem:** Find the domain of $f(x)=\frac{7-3x}{4x-9}$.\n\n2. **Formula/rule:** A rational function is undefined when its denominator is $0$.\nSo we set the denominator equal

1. **State the problem:** We need to find the domain of the function $$f(x) = \frac{7 - 3x}{4x - 9}$$.\n\n2. **Recall the domain rule for rational functions:** The domain includes

1. **State the problem.** We are finding the range of $y=\frac{\sqrt{6x^2+11x-7}}{\sqrt{|2x-5|+4x^2-2x-13}}$.

1. **State the problem.** We need the domain of $$y=\frac{\sqrt{6x^2+11x-7}}{\sqrt{|2x-5|+4x^2-2x-13}}$$.

1. Problema: Dividir $$3x^3 + 4x^2 - 3x + 2$$ entre $$x + 2$$ usando división sintética. 2. Para división sintética con divisor $$x + 2$$, usamos $$-2$$ como valor para la división

1. Problema: Dividir $3x^3 + 4x^2 - 3x + 2$ entre $x + 2$ usando división sintética. 2. Recordemos que para división sintética con divisor $x - r$, usamos $r$; aquí divisor es $x +

1. **Problem statement:** Find the quotient and simplify for problems 28 to 41. 2. **Recall division of fractions:** Dividing by a fraction is the same as multiplying by its recipr

1. **Problem Statement:** Let's solve a simple algebraic equation: Find $x$ if $$2x + 3 = 11$$. 2. **Formula and Rules:** To solve for $x$, we use the rule of isolating the variabl

1. Let's consider the numerical pattern: $2, 4, 6, 8, 10, \ldots$ 2. Observe that each number increases by $2$ from the previous number.

1. **Nyatakan masalah:** Tukarkan persamaan berikut kepada bentuk linear $$Y = mX + c$$ dan nyatakan kecerunan (gradient) serta pintasan-y (y-intercept). ---

1. **State the problem:** Solve the equation $$\frac{2e^x+e^{-x}}{e^x+1} = 4$$ for $x$, giving the answer correct to 3 decimal places. 2. **Rewrite the equation:** Let $y = e^x$. S

1. **State the problem:** Simplify and verify the equation $$2 \log_2 \sqrt{x} + 2 \log_2 y = \log_2 xy$$ and show that it is equivalent to $$\log_2 x + \log_2 y^2 = \log_2 xy$$. 2

1. **Énoncé du problème** : On a la matrice

1. **Stating the problem:** We need to identify which of the given statements A, B, C, or D is not true. 2. **Recall important exponent rules:**