🧮 algebra

1. The problem is to simplify the expression $$-54 - (-54)$$. 2. Recall that subtracting a negative number is the same as adding its positive counterpart, i.e., $$-(-54) = +54$$.

1. The problem asks us to evaluate the expression: $-13 - (-30)$. 2. Recall that subtracting a negative number is equivalent to adding its positive counterpart.

1. The problem states that 14 workers can build a wall in 42 days. We need to find how many days 1 worker will take to build the same wall. 2. Since 14 workers take 42 days, the to

1. Stating the problem: We know that 14 workers can build a wall in 42 days, and we need to find out how many days it will take for one worker to build the same wall. 2. Understand

1. Stating the problem: Solve the equation $-4x=4$ for $x$. 2. Isolate $x$ by dividing both sides of the equation by $-4$:

1. Énoncé du problème : Nous avons deux nombres rationnels non nuls $x$ et $y$ qui satisfont les équations :

1. **State the problem:** Simplify the expression $$\frac{2}{8} - \frac{13}{4} + \frac{17}{2} + 12$$. 2. **Simplify fractions where possible:** $$\frac{2}{8} = \frac{1}{4}$$, so th

1. Let's clarify the problem: it seems you're asking whether to factorize first in the expression or equation involving 2.2. 2. Generally, when solving algebraic problems or simpli

1. **State the problem:** We are given that $(a - b) = 5$ and $ab = 28$. We need to find the value of $a^3 - b^3$. 2. **Recall formula:** The difference of cubes can be factored as

1. Stating the problem: A pump fills a tank in 2 hours, but due to a leak, it takes 2.5 hours to fill the tank. We need to find how long the leak alone would take to empty the full

1. Given the problem: If $x + \frac{1}{x} = 11$, find the value of $x^2 + \frac{1}{x^2}$. 2. Start by squaring both sides of the equation to involve $x^2$ and $\frac{1}{x^2}$:

1. Énonçons le problème : Soient $x$ et $y$ deux réels. Nous avons deux conditions :

1. Let's state the problem: We want to find when $3\cdot(x+1)$ is a factor of $x^n + 1$. 2. Note that to check if $(x+1)$ is a factor of $x^n + 1$, by the Factor Theorem, $(x+1)$ i

1. **State the problem:** We are given the equation $x^2 + kx + 6 = (x + 2)(x + 3)$ and need to find the value of $k$ such that the equality holds for all $x$. 2. **Expand the righ

1. Stating the problem: We are given that 12 sheets of thick paper weigh 40 grams, and we need to find how many sheets weigh 1 gram. 2. Find the weight of one sheet by dividing the

1. We are asked to solve the inequality $$7 - x \leq 9$$. 2. Start by isolating $x$ on one side. Subtract 7 from both sides:

1. We are asked to find the cube root of 8. 2. The cube root of a number $x$ is a number $y$ such that $y^3 = x$.

1. Énonçons le problème : résoudre l'exercice 2 (sans indication spécifique, supposons un problème algébrique classique). 2. S'il s'agit d'une équation à résoudre (exemple : $2x +

1. **State the problem:** Simplify the expression $$6a + 6b + 9c - 4a + 9b - 2c$$. 2. **Group like terms:** Combine terms with the same variables.

1. Énoncé du problème : Vous souhaitez pratiquer les mathématiques. Voici un problème simple d'algèbre pour commencer. 2. Problème : Résoudre l'équation linéaire suivante : $$2x +

1. We are given the inequality $5 > 3$ and asked to multiply both sides by $-3$ and then compare the results. 2. Multiplying both sides by $-3$, we get: