🧮 algebra

1. نبدأ بحل السؤال الأول: "أقل من مثلي عدد بمقدار خمسة يساوي 12". 2. نترجم الجملة إلى معادلة:

1. نبدأ بترجمة الجملة: "أقل من مثلي عدد بمقدار خمسة يساوي 12". 2. لنفترض أن العدد هو $ن$.

1. **State the problem:** Multiply the fractions $\frac{2}{3}$ and $4 \frac{1}{2}$.\n\n2. **Convert mixed number to improper fraction:**\n$4 \frac{1}{2} = \frac{4 \times 2 + 1}{2}

1. **State the problem:** Solve the equation $\frac{m}{3} = -12$ for $m$. 2. **Formula and rule:** To isolate $m$, multiply both sides of the equation by 3, because $m$ is divided

1. **State the problems:** Solve the linear equations from question 9 to 13. 2. **General formula and rules:** For linear equations of the form $ax + b = c$, isolate $x$ by subtrac

1. The problem asks to convert 3.2 million to a fraction of a million. 2. We start with the number 3.2 million, which means 3.2 times 1,000,000.

1. **State the problem:** Simplify the expression $$2 k^5 \times k^4 \times \frac{1}{2} k^7$$. 2. **Recall the rule for multiplying powers with the same base:** When multiplying te

1. **State the problem:** We need to put the fractions $\frac{7}{10}$, $\frac{8}{15}$, and $\frac{3}{5}$ in ascending order. 2. **Find a common denominator:** To compare fractions,

1. **State the problem:** We need to put the fractions $\frac{47}{100}$, $\frac{9}{20}$, and $\frac{4}{10}$ in ascending order. 2. **Find a common denominator:** To compare fractio

1. **State the problem:** Simplify the expression $$- \frac{1}{2} n^2 \times - \frac{1}{2} n^6 \times n^7$$. 2. **Recall the rules:** When multiplying powers with the same base, ad

1. **State the problem:** Find all functions $f : \mathbb{Z} \to \mathbb{Z}$ such that $$f(f(n)) + f(n+1) = 2n + 3$$

1. The problem is to find the roots of the quadratic function $f(x) = -2x^2 - 8x - 3$ and describe its graph. 2. The roots of a quadratic function $ax^2 + bx + c = 0$ are found usi

1. Problema: Determinar el dominio y bosquejar la gráfica de la función \(h(x) = \sqrt{1 - x^3}\). 2. Para funciones con raíz cuadrada, el radicando debe ser mayor o igual a cero p

1. **State the problem:** Simplify the expression $$12\sqrt{10} \div 2$$. 2. **Recall the rule:** Division can be written as multiplication by the reciprocal. Here, dividing by 2 m

1. **State the problem:** Find the positive solution of the equation $$7x^{\frac{5}{3}} + 27 = 54459$$. 2. **Isolate the term with the variable:** Subtract 27 from both sides:

1. **State the problem:** Find the positive solution of the equation $$4x^{\frac{7}{8}} - 13 = 499$$. 2. **Isolate the term with the fractional exponent:** Add 13 to both sides:

1. **State the problem:** Solve for all values of $x$ in the equation $$\sqrt{x + 1} = \sqrt{x + 8}.$$\n\n2. **Understand the equation:** Both sides are square roots. For the equat

1. **State the problem:** Solve the equation $$\sqrt{x + 1} = \sqrt{x + 8}$$ for all values of $x$. 2. **Recall the property of square roots:** If $$\sqrt{A} = \sqrt{B}$$, then $$A

1. **State the problem:** Complete the square for a quadratic expression, typically in the form $ax^2 + bx + c$. 2. **Formula and rules:** To complete the square for $x^2 + bx + c$

1. **State the problem:** Simplify or analyze the quadratic expression $2x^2 - 5x + 2$. 2. **Recall the quadratic formula:** For any quadratic equation $ax^2 + bx + c = 0$, the sol

1. The problem is to solve for $x$ in the equation $$\frac{1}{2x} + \frac{3}{x} = y.$$\n\n2. To solve for $x$, first find a common denominator for the fractions on the left side. T