🧮 algebra

1. **State the problem:** We need to find which two expressions correctly represent the inequality $$-3(2x - 5) < 5(2 - x)$$. 2. **Expand both sides:**

1. **State the problem:** Solve for $u$ in the equation $$-\frac{4}{5}u = -12$$. 2. **Recall the multiplicative property of equality:** To isolate $u$, multiply both sides of the e

1. **State the problem:** Solve the linear equation $$7u = -\frac{14}{3}$$ for $$u$$. 2. **Formula and rule:** To isolate $$u$$, use the multiplicative property of equality which s

1. El paso 4 se refiere a simplificar o cancelar factores comunes en una expresión matemática. 2. Por ejemplo, si tienes una fracción como $$\frac{6x}{3x}$$, puedes cancelar el fac

1. **State the problem:** Solve the quadratic equation $x^2 - 3x = -2$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** Evaluate the expression $$T = 16 + 4(2(5-4))$$. 2. **Recall the order of operations:** Parentheses first, then multiplication, and finally addition.

1. The problem is to illustrate the trend line given by the equation $$y = -\frac{4}{5}x + 94$$. 2. This is a linear equation in slope-intercept form $$y = mx + b$$, where $$m$$ is

1. **Problema:** Donats els nombres reals $a$ i $b$ amb $a+b=1$, i altres igualtats contradictòries $a+b=6$ i $a+b=7$, i valors assignats a variables $x, y, z$ i altres, es demana

1. **State the problem:** Solve the equation $$\frac{x}{x^2 - 4x - 12} - \frac{1}{x+2} = \frac{5}{x+2}$$ for $x$. 2. **Factor the quadratic denominator:**

1. **Solve the equation:** $\frac{1}{2x} = \frac{5}{4x} - \frac{1}{x^2}$. 2. The LCD (Least Common Denominator) for the terms is $4x^2$.

1. **Problem Statement:** Solve the equations in parts b, c, d, e, and factorise and simplify in parts f and g as requested. ---

1. **Problem statement:** Given a cubic function $f(x) = ax^3 + bx^2 + cx + d$, find the stationary points, determine their nature, find the point of inflexion, and sketch the grap

1. Let's start by stating the problem: How to factor an algebraic expression. 2. Factoring means rewriting an expression as a product of simpler expressions.

1. Le problème consiste à associer chaque graphique d'une fonction exponentielle à ses paramètres $a$ et $c$. 2. La fonction exponentielle générale est $y = a c^x$ avec $c > 0$ et

1. The problem is to find the square root of a number, which means finding a value that, when multiplied by itself, gives the original number. 2. The formula for the square root of

1. Problemet: Vi skal omskrive et udtryk, der indeholder en tæller, til et kvadrat. 2. Formlen: Hvis vi har et udtryk af formen $a^2 + 2ab + b^2$, kan det omskrives som $(a+b)^2$.

1. **State the problem:** We are given two sets defined by functions of $x$ where $x$ is a natural number from 1 to 4. Set $M = \{4x \mid x \in \mathbb{N}, 1 \leq x \leq 4\}$ and s

1. **Opgave 4: Omskriv til produkt via kvadratsætningerne** Vi bruger kvadratsætningerne:

1. **Problem statement:** We will rewrite and reduce expressions using the square formulas (kvadratsætningerne). 2. **Square formulas used:**

1. **Problem statement:** We are asked to rewrite and reduce algebraic expressions using the square formulas (kvadratsætningerne). 2. **Square formulas used:**

1. **State the problem:** Joanie has 50.75 dollars and buys three items: a burger, a souvenir, and a pass. The burger costs \(\frac{1}{6}\) as much as the souvenir, and the souveni