🧮 algebra

1. Stating the problem: Solve the quadratic equation $$0 = x^2 - 6x + 9$$. 2. Formula and rules: The quadratic equation is in standard form $$ax^2 + bx + c = 0$$ where $$a=1$$, $$b

1. Vamos resolver um problema de álgebra envolvendo uma equação do primeiro grau. 2. Suponha que o problema seja: "Resolva a equação $2x + 3 = 11$."

1. **State the problem:** Solve the equation $2x + 10 = 4x - 10$ for $x$. 2. **Write down the equation:**

1. **State the problem:** Solve the equation $2x + 20 = 4x - 10$ for $x$. 2. **Write down the equation:**

1. **State the problem:** Factor the trinomial $$15n^2 - 27n - 6$$ completely. 2. **Recall the factoring formula:** For a quadratic trinomial $$ax^2 + bx + c$$, we look for two num

1. **State the problem:** Solve the system of linear equations: $$x = 16 - 4y$$

1. **State the problem:** Simplify the expression $\frac{x+2}{x^2-4}$. 2. **Recall the formula and rules:** The denominator is a difference of squares, which factors as $a^2 - b^2

1. The problem states that $y$ varies directly as $x$, which means the relationship can be written as $y = kx$ where $k$ is a constant. 2. We are given that $y = 21$ when $x = 6$.

1. **State the problem:** Solve the equation $ (x-2)^2 - 9 = 0 $ for $ x $. 2. **Use the formula:** Recognize this as a quadratic equation in the form $ (a)^2 - b^2 = 0 $, which ca

1. The problem asks to find the function rule for $g(x)$, which is a transformation of $f(x) = |x|$. 2. The general form for transformations of the absolute value function is:

1. The problem asks to find the function rule for $g(x)$, which is a translation of the absolute value function $f(x) = |x|$. 2. The general form for a translated absolute value fu

1. **State the problem:** Solve the equation $$\frac{x + 6}{x - 5} = \frac{5}{4}$$ for $x$. 2. **Use the cross-multiplication method:** When two fractions are equal, their cross pr

1. **State the problem:** Solve the equation $$\frac{4}{x+6} = \frac{5}{4x-8}$$ for $x$ and simplify the answer fully. 2. **Use the cross-multiplication formula:** For equations of

1. **State the problem:** Simplify the expression $5x(x-1)-4(x+1)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside.

1. **State the problem:** Convert the equation $2x - 3y = 5$ to slope-intercept form $y = mx + b$. 2. **Recall slope-intercept form:** The slope-intercept form is $y = mx + b$, whe

1. Stating the problem: Calculate the value of the expression $$\frac{\left(\frac{3}{7} + \frac{1}{2}\right)^2 \cdot \left(2 - \frac{1}{3}\right)^2 - 1}{\left(\frac{1}{6} - 1\right

1. Planteamos el problema: Tenemos la función $f(x) = \frac{2x}{2-x}$ y queremos encontrar la función compuesta $f(f(x))$. 2. Recordemos que la función compuesta $f(f(x))$ signific

1. **State the problem:** Find the slope $m$ of the line passing through the points $(-5,12)$ and $(9,-10)$ in the form $y=mx+b$. 2. **Formula for slope:** The slope $m$ between tw

1. **State the problem:** Gillian has three test scores. The first is 90, the second is 75, and the third is unknown. We want to find the lowest score on the third test so that the

1. **State the problem:** We want to find how much bigger 500 is compared to 450, expressed as a percentage. 2. **Understand the idea:** To find how much bigger one number is than

1. **State the problem:** We want to find what percent 500 is more than 450. 2. **Formula:** The percent increase from a number $a$ to a number $b$ is given by: