🧮 algebra

1. **State the problem:** Simplify the expression $$0.7(-6x + 7x + 6) - 0.7x$$. 2. **Apply the distributive property:** Multiply 0.7 by each term inside the parentheses.

1. **Enunciado do problema:** Resolver a inequação $$\frac{1}{3}(x - 6) \geq -\frac{5x - 2}{4} + 2$$ e apresentar o conjunto-solução em forma de intervalo. 2. **Passo 1: Eliminar o

1. **State the problem:** Simplify the expression $$6(-0.3b - 5b + 3) - 4b$$. 2. **Use the distributive property:** Multiply 6 by each term inside the parentheses.

1. **State the problem:** Solve the inequality $$y + \frac{7}{8} > \frac{3}{4}$$. 2. **Formula and rules:** To isolate $y$, subtract $\frac{7}{8}$ from both sides of the inequality

1. **State the problem:** Solve the inequality $$w + \frac{1}{2} \geq -\frac{2}{5}$$ for $$w$$. 2. **Formula and rule:** To isolate $$w$$, use the additive property of inequality w

1. **State the problem:** Solve the inequality $$6x \geq 3 + 4(2x - 1)$$ and identify the correct representations. 2. **Expand the right side:**

1. **State the problem:** Solve the inequality $$3(8 - 4x) < 6(x - 5)$$ and determine which number line represents the solution set. 2. **Apply the distributive property:**

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