🧮 algebra

1. The problem is to simplify the expression $$\frac{2x}{3} = \frac{-1}{3}$$. 2. This is an equation where the fraction on the left side equals the fraction on the right side.

1. The problem is to find the sum of the integers from 1 to 10. 2. We use the formula for the sum of the first $n$ natural numbers: $$S = \frac{n(n+1)}{2}$$ where $n$ is the last n

1. The problem is to solve the equation $$\frac{2x}{3} = \frac{1}{3}$$ for $x$. 2. To solve for $x$, we use the property that if two fractions are equal and have the same denominat

1. **State the problem:** Expand and simplify the expression $$6y(5y + 4) - 5y(2y - 7)$$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the t

1. **State the problem:** Simplify the expression $$6y(5y + 4) - 5y(2y - 7)$$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the term outside.

1. **State the problem:** Factorise the expression $$(5x - 3)(14x - 4) - (7x - 2)^2$$. 2. **Recall the formulas:**

1. **Énoncé du problème :** Développer et simplifier l'expression $$\left(\sqrt{x} + \sqrt{1-x}\right)^2$$. 2. **Formule utilisée :** Pour développer un carré de somme, on utilise

1. **State the problem:** Simplify the expression $$\frac{x + 1}{2x + 9} - \frac{2x + 3}{4x - 1}$$. 2. **Find a common denominator:** The denominators are $2x + 9$ and $4x - 1$. Th

1. Énonçons le problème : développer et simplifier l'expression $$\left(\sqrt{x} + \sqrt{1-x}\right)^2$$. 2. Rappel de la formule : $$(a+b)^2 = a^2 + 2ab + b^2$$.

1. **State the problem:** Calculate the value of the expression $(-12) + 89 + (-28)$.\n\n2. **Recall the rules:** Adding a negative number is the same as subtracting its absolute v

1. **Problem:** Simplify and expand the expression $(3a + 2b)(5a - 7b)$. 2. **Formula:** Use the distributive property: $(x + y)(z + w) = xz + xw + yz + yw$.

1. **State the problem:** Simplify the expression $$(3a+2a)(5a-7b)$$. 2. **Combine like terms inside the parentheses:**

1. The problem asks: What is the ordered pair that corresponds to $x = -2$ for the equation $2x + y = 4$? 2. The equation given is $2x + y = 4$. We want to find $y$ when $x = -2$.

1. **State the problem:** Factorize the expression $$(x+4)(3x+11)-(x+4)(6x+7)$$. 2. **Identify common factors:** Notice that both terms have a common factor of $$(x+4)$$.

1. **State the problem:** Simplify the expression $$(x+4)(3x+11) - (x+4)(6x+7).$$ 2. **Formula and rule:** Use the distributive property: $$a(b+c) = ab + ac$$ and factor common ter

1. Énoncé du problème : Réduire sous forme d'une écriture fractionnaire les expressions suivantes. 2. Pour additionner ou simplifier des expressions fractionnaires, il faut trouver

1. The problem is to find the solutions of an equation (not specified by the user). 2. Since the equation is not given, I cannot provide specific steps or solutions.

1. Problem: Solve the inequality $$\log_{\frac{1}{5}}(x - 5) > -2$$. 2. Formula and rules: For logarithmic inequalities with base $a$ where $0 < a < 1$, the inequality direction re

1. **State the problem:** Simplify the expression $$1 - 9 \times 2^2$$. 2. **Recall the order of operations:** According to PEMDAS (Parentheses, Exponents, Multiplication and Divis

1. Solve the quadratic equation $x^2 - 5x + 6 = 0$. 2. Use the factoring method: find two numbers that multiply to $6$ and add to $-5$.

1. Problem: Cijena automobila je snizena prvo za 10%, a zatim za dodatnih 8%, i sada je cena 2482. Treba da nađemo prvobitnu cenu automobila. 2. Formula: Ako je prvobitna cena $P$,