🧮 algebra

1. **State the problem:** Simplify the expression $$(2v^2 - 9v + 9) + (4v^2 - 8v + 5) - (-7v^2 + 5v + 5)$$ 2. **Apply the distributive property:** Remove parentheses and change sig

1. **State the problem:** Solve the inequality $$-4 \leq 3x - 1$$ for $$x$$. 2. **Add 1 to both sides** to isolate the term with $$x$$:

1. **State the problem:** Factor the monic quadratic trinomials and determine if they are prime over the integers. 2. **Recall the formula and rules:** For a trinomial $x^2 + bx +

1. **State the problem:** Factor the monic quadratic trinomials $x^2 + 5x - 14$ and $x^2 - 6x + 8$ and determine if they are prime over the integers. 2. **Recall the factoring rule

1. The problem is to identify the inequality represented by each number line graph. 2. The first number line has a filled circle at 25 and an arrow pointing left, indicating all va

1. **Problem:** Andre claims that the expressions $10x + 6$ and $5x + 11$ are equivalent because both equal 16 when $x=1$. 2. **Formula and rule:** Two expressions are equivalent i

1. **State the problem:** We need to find a 3-digit number with digits $a$, $b$, and $c$ such that: - The first digit $a$ is twice the third digit $c$.

1. **State the problem:** We are given values $x=11$, $y=5.5$, and $z=2$. We need to find the final number after performing the following operations: double $x$, divide by $8y$, mu

1. **State the problem:** Solve the equation $$6 + \frac{4}{5}b = \frac{9}{10}b$$ for the variable $b$. 2. **Write down the formula and rules:** We want to isolate $b$ on one side.

1. **State the problem:** Solve the equation $$x + \frac{3}{5} = \frac{3}{5}$$ for $x$. 2. **Formula and rules:** To isolate $x$, subtract $\frac{3}{5}$ from both sides of the equa

1. **State the problem:** We are given the function $$g(x) = \frac{x^2 - 4x + 8}{3x - 15}$$ and we want to analyze or simplify it. 2. **Identify the formula and rules:** This is a

1. **Planteamiento del problema:** Un comerciante necesita comprar 120 litros de leche usando solo envases de 1 litro y 1 1/2 litros para minimizar su gasto.

1. El problema pide reducir la expresión algebraica dada en el ejercicio 17. 2. La expresión es:

1. **State the problem:** Simplify the expression \(\frac{y-x}{x^2 y^3}\). 2. **Recall the formula and rules:** When simplifying algebraic fractions, divide each term in the numera

1. The problem is to reduce each fraction to its simplest form by dividing numerator and denominator by their greatest common divisor (GCD). 2. The formula to reduce a fraction $\f

1. **State the problem:** Solve the inequality $$89 - f \geq 86$$ for the variable $f$. 2. **Isolate the variable:** To solve for $f$, we want to get $f$ alone on one side of the i

1. **State the problem:** Solve the inequality $$-2 \leq -78 - p$$ for $$p$$. 2. **Isolate the variable:** To solve for $$p$$, we want to get $$p$$ alone on one side of the inequal

1. Planteamos el problema: resolver y graficar las funciones dadas, e indicar dominio y rango. 2. Para funciones lineales como a) y b), la fórmula general es $y = mx + b$, donde $m

1. **State the problem:** Calculate Social Security (SS) tax, Medicare tax, and total deductions for given gross pay values using the tax rates. 2. **Formulas and tax rates:**

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. The formula used here is to isolate $x$ by performing inverse operations. We subtract 3 from both sides and then d

1. **State the problem:** Simplify the expression $$9 - 45 \cdot \frac{7}{5} - \left[12 + 7 - 21 \cdot \frac{9}{3}\right]$$. 2. **Recall order of operations:** Perform multiplicati