🧮 algebra

1. Énoncé du problème : Réduire les expressions algébriques données en combinant les termes semblables. 2. Rappel de la règle : Pour réduire une expression algébrique, on additionn

1. **State the problem:** We are given the function $f(x) = 5 - 2x$ and want to understand its properties. 2. **Formula and rules:** This is a linear function of the form $f(x) = m

1. **State the problem:** Fully factorise the quadratic expression $2x^2 + 13x + 15$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers

1. The user requested graphs of functions but did not specify which functions to graph. 2. To provide graphs, please specify the functions you want to see plotted.

1. **Problem Statement:** Find the natural domain and analyze the functions given in exercises 15 to 20. 2. **Function 15: $f(x) = 5 - 2x$**

1. **State the problem:** Fully factorise the quadratic expression $$3t^2 + 16t + 5$$. 2. **Recall the factoring method:** For a quadratic $$at^2 + bt + c$$, we look for two number

1. **Problem 15: Find the natural domain and graph of** $f(x) = 5 - 2x$. - This is a linear function.

1. **State the problem:** Solve the equation $$|x| = x^2 + x - 3$$. 2. **Recall the definition of absolute value:**

1. **State the problem:** Solve the equation $$\sqrt{7} \cdot \frac{\log n}{\log 2} - \frac{\log 2n}{\log 2} = 1$$ for $n$. 2. **Recall logarithm properties:**

1. **Problem statement:** The mass of a radioactive substance decreases exponentially at a rate of 3% each day. We need to find the overall percentage decrease after 10 days. 2. **

1. Let's start by understanding what percentage increase and decrease mean. 2. Percentage increase is used when a value goes up. The formula is:

1. We are asked to determine the function rule (voorschrift) of a homographic function given certain conditions. 2. A homographic function has the general form:

1. Let's clarify the concept of "rise over run." 2. "Rise over run" is a way to describe the slope of a line in coordinate geometry.

1. **State the problem:** Solve the equation $x(x + 5) - 12 = x^2 + 3x$. 2. **Write the equation:**

1. **State the problem:** Solve the equation $3 + x = 1 + 4x$ for $x$. 2. **Write down the equation:**

1. **State the problem:** Solve the inequality $x > 7 - 4$ and represent the solution on a number line. 2. **Simplify the inequality:**

1. **State the problem:** Solve the inequality $$-6 \leq x - 5 < 1$$. 2. **Understand the inequality:** This is a compound inequality involving $x$. We want to find all values of $

1. **State the problem:** Simplify the expression $$\frac{x^3}{2y^2} \cdot \frac{6y^4}{xy}$$. 2. **Write the expression:** $$\frac{x^3}{2y^2} \times \frac{6y^4}{xy}$$.

1. **State the problem:** Simplify the expression $$\frac{a + 1}{a^{2}-4} + \frac{1 - a^{2}}{(a-1)^{2} + 3}$$. 2. **Recall important formulas and rules:**

1. **State the problem:** Simplify the expression $$\frac{16x^2 + 24x + 9}{3x^2 + 13x - 10} \cdot \frac{6x^2 + 25x - 25}{4x^2 - 13x - 12}$$

1. **Problem:** Solve the equation $$|1 - 2m| = m + 2$$ and verify the solutions. 2. **Formula and rules:** The absolute value equation $$|A| = B$$ implies two cases if $$B \geq 0$