🧮 algebra

1. Problem: Add the integers given in each expression. 2. Formula: For any two integers $a$ and $b$, addition is $a + b$.

1. **State the problem:** Simplify the expression $\frac{5x^2}{5x}$.\n\n2. **Recall the rule:** When dividing powers with the same base, subtract the exponents: $\frac{a^m}{a^n} =

1. Problem: Add the integers given in the first expression: $(+73) + (+64)$. 2. Formula: Integer addition is straightforward: add the numbers if they have the same sign, subtract i

1. **State the problem:** Solve the quadratic equation $$5x^2 + 10x - 45 = 0$$ by completing the square. 2. **Divide the entire equation by 5** to simplify the coefficient of $$x^2

1. **Problem 1: List subsets of the set \{4, 5, 6\}** The subsets of a set include the empty set, single-element sets, two-element sets, and the full set itself.

1. **State the problem:** Solve the quadratic equation $x^2 + 6x - 14 = -2$. 2. **Rewrite the equation:** Move all terms to one side to set the equation equal to zero:

1. **State the problem:** Simplify the expression $$w^{-\frac{1}{7}} \cdot w^{-\frac{12}{5}}$$ assuming all variables are positive. 2. **Recall the rule for multiplying powers with

1. **State the problem:** Simplify the expression $$x^{-\frac{17}{6}} \times x^{-\frac{11}{5}}$$ and write the answer in the form $$A$$ or $$\frac{A}{B}$$ where $$A$$ and $$B$$ are

1. **Problem 1: Solve $x^3 - 64 = 0$** This is a difference of cubes since $64 = 4^3$. The formula for difference of cubes is:

1. **State the problem:** Simplify the expression $10m^2 \cdot 3m^5$ without negative exponents. 2. **Recall the rule for multiplying powers with the same base:** When multiplying

1. **State the problem:** Simplify the expression $$\frac{6x^{10}y}{2x^{7}y^{3}}$$ using properties of exponents. 2. **Recall the properties of exponents:**

1. **State the problem:** Solve the inequality $$\frac{-x^2}{4x - 1} \geq \frac{2}{x - 9}$$ using an interval table. 2. **Rewrite the inequality:** Bring all terms to one side to c

1. The problem asks: Josie has 47 left in her checking account and writes a check for 55. What is her new balance? 2. Writing a check for 55 means subtracting 55 from her current b

1. **State the problem:** Simplify the expression $$-(3ab + b^2 - 5a^2 b) + (a^2 - 5ab + 2b^2) - (a^2 b - 3a^2 + b^2)$$. 2. **Remove parentheses carefully, applying signs:**

1. **State the problem:** Find the value of $x$ such that $$1000^4 = 10^x.$$\n\n2. **Rewrite the base 1000 in terms of 10:** Since $1000 = 10^3$, we can write $$1000^4 = (10^3)^4.$

1. **State the problem:** Solve the equation $6y + 11 = 3y + 5$ for $y$. 2. **Isolate the variable terms:** Subtract $3y$ from both sides to get all $y$ terms on one side.

1. The problem is to find the value of 26% as a decimal or fraction. 2. Percent means per hundred, so 26% means 26 out of 100.

1. Énonçons le problème : Calculer $-1,5 \times \left((-2,8)^2 - 9,2 + 3,6\right)$ et vérifier si le résultat est égal à 20,16. 2. Rappelons la formule et les règles importantes :

1. The problem is to make the right-hand side (rhs) equal to the left-hand side (lhs) of an equation. 2. To do this, we need to identify the equation and then manipulate one side t

1. **State the problem:** There are 36 cookies in total. The number of peanut butter cookies equals the sum of all other types. There are 4 more sugar cookies than chocolate chip c

1. **State the problem:** Find the slope of the line passing through the points $(-6, -12)$ and $(8, -14)$. 2. **Recall the slope formula:** The slope $m$ between two points $(x_1,