🧮 algebra

1. **State the problem:** Solve the linear equation $2x - 1 = 3$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate the variable by performing inverse operations. Additio

1. **Problem Statement:** X, Y, and Z are software experts who work on upgrading software. Each takes a day off after a fixed number of workdays: X after 3 days, Y after 4 days, an

1. **Problem Statement:** We have two brands of oil, X and Y, made from components A, B, and C.

1. **State the problem:** Find the inverse function $f^{-1}(x)$ of the function $$f(x) = \frac{2 - 3x}{x + 1}.$$ 2. **Recall the formula and method for finding inverses:** To find

1. Let's clarify the problem: You are asking about the origin of the coordinate -2 in the answer to question 6b. 2. Typically, coordinates like -2 come from solving equations or ev

1. **State the problem:** Find the value(s) of $x$ when $-2x^2 - 5x + 7 = 0$. 2. **Formula used:** This is a quadratic equation of the form $ax^2 + bx + c = 0$. The solutions are g

1. **State the problem:** Solve the equation $X - Y = 0$ for $X$ in terms of $Y$. 2. **Formula and rules:** The equation is a simple linear equation. To isolate $X$, add $Y$ to bot

1. The problem is to provide a step-by-step explanation for a math question, but since no specific question was given, I will demonstrate how to solve a simple algebraic equation s

1. The problem is to analyze the function $y = x^2$. 2. This is a quadratic function, which generally has the form $y = ax^2 + bx + c$. Here, $a=1$, $b=0$, and $c=0$.

1. Diketahui fungsi $g(x) = \frac{12}{mx + n}$ dengan kondisi $g(1) = -4$ dan $g(3) = -12$. Kita diminta mencari nilai $x$ yang memenuhi $g(x) = x$. 2. Dari $g(1) = -4$, kita subst

1. **State the problem:** We are given the nth term of a sequence as $$T(n) = 3n^2 + 8$$ and told that a term in this sequence has a value of 83. We need to find the position $$n$$

1. The problem involves factoring the expression $12x^2 + 2x$. 2. To factor, we look for the greatest common factor (GCF) of the terms.

1. **State the problem:** We want to complete the proof for the formula

1. **State the problem:** Jennifer thinks of a number $h$. She triples it and then subtracts 11 to get an answer that is less than 34. 2. **Write the inequality:** Tripling $h$ mea

1. **State the problem:** We are given the equation $x(r - 7) + 3 = 17x + 25$ where $r$ is a positive integer. We want to find the values of $r$ for which the equation has exactly

1. **State the problem:** We are given the equation $$h = \frac{9(v - 273.15)}{5} + 32$$ which converts temperature from kelvins ($v$) to degrees Fahrenheit ($h$). We need to find

1. The problem is to expand the expression $ (3x - 2y)^2 $. 2. We use the formula for the square of a binomial: $$ (a - b)^2 = a^2 - 2ab + b^2 $$ where $a = 3x$ and $b = 2y$.

1. **State the problem:** Solve the inequality $x^2 - 5x + 6 < 0$. 2. **Recall the formula:** For quadratic inequalities, first find the roots of the quadratic equation $x^2 - 5x +

1. **State the problem:** We want to express $\frac{1}{20\sqrt{20}}$ in the form $\frac{\sqrt{5}}{n}$, where $n$ is a positive integer. 2. **Rationalise the denominator:** Start wi

1. Дано равенство: $x^2 - 5x + 6 = (x - 2)(x - 3)$. 2. Это равенство показывает, что многочлен второй степени $x^2 - 5x + 6$ можно разложить на произведение двух линейных множителе

1. **State the problem:** Solve the equation $$\frac{5x^2}{2} + 47 = 137$$ for $x$. 2. **Isolate the term with $x^2$:** Subtract 47 from both sides: