🧮 algebra

1. **State the problem:** Use the distributive property of multiplication over subtraction to simplify expressions like $$4 \frac{1}{2} \left( \frac{2}{3} - 1 \frac{3}{5} \right)$$

1. **State the problem:** We need to subtract the polynomial $$(-5x^6 + 4x^4 + 2x)$$ from $$8x^6 - 10x^4 - 3x$$. 2. **Write the expression:**

1. **State the problem:** Find the difference and write the answer in standard form for the expression $$(9a^2 + 2a) - (4a^2 + 3 - a)$$. 2. **Apply the subtraction:** Distribute th

1. **State the problem:** Simplify and identify the property used in the expression $$4 \frac{1}{3} \left( \frac{2}{5} - \frac{1}{3} \right)$$. 2. **Recall the distributive propert

1. **State the problem:** Solve the linear equation $3x + 7y = 21$ for $y$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation by moving other term

1. **State the problem:** Lorna took three friends to the zoo, so there are 4 people in total (Lorna + 3 friends). 2. **Given information:**

1. **State the problem:** Determine if the functions $f(x) = 3x + 1$ and $g(x) = x - \frac{1}{3}$ are inverses of each other. 2. **Recall the rule for inverse functions:** Two func

1. **State the problem:** Solve the equation $$\frac{-98}{15} + 6.2 = t - 3$$ 2. **Rewrite the equation:**

1. **Stating the problem:** We want to understand how to factor trinomials and identify conditions for perfect square trinomials. 2. **Factoring a trinomial:** A trinomial of the f

1. The problem asks to find the equation that represents the hanger diagram described. 2. The diagram consists of a vertical yellow rectangular bar labeled 9 on the inside left.

1. The problem is to find the values that fill in the blanks in a given expression or equation. 2. Since the user did not provide a specific equation or expression, I cannot solve

1. **State the problem:** Winterfield Bike Shop pays 420 for a bicycle and marks up the price by 17.2% to find the retail price. 2. **Formula used:** Retail price = Cost price + Ma

1. Das Problem lautet: Löse die Gleichung Nr. 3 (bitte spezifiziere die Gleichung, falls vorhanden). 2. Da keine konkrete Gleichung gegeben ist, kann ich nur allgemein erklären, wi

1. Problem: a) Gib zwei Terme an, die den Flächeninhalt des Rechtecks beschreiben. 2. Ein Rechteck hat Seitenlängen $x+2$ und $x+3$. Der Flächeninhalt $A$ ist das Produkt der Seite

1. **State the problem:** Find the inverse of the relation given by the set of ordered pairs $\{(-3,-7), (0,-1), (5,9), (7,13)\}$ and determine if the inverse is a function. 2. **R

1. **State the problem:** We need to identify which scenarios can be described by the number $-300$. 2. **Understand the meaning of negative numbers:** Negative numbers often repre

1. **State the problem:** The temperature was initially $-16$ degrees and it rose by $23$ degrees. We need to find the new temperature. 2. **Formula and concept:** When a temperatu

1. The problem states that a football team was on the 35 yard line and lost 12 yards on a play. 2. We need to find the integer that represents the new position after losing 12 yard

1. **State the problem:** Blaine withdraws 78 from his bank account, but he only had 60 in the account. We want to find the new account balance using an integer. 2. **Understand th

1. **State the problem:** Simplify the expression $$6x - 8 - 4x + 2$$ by grouping like terms. 2. **Identify like terms:** Variable terms contain $$x$$ and constant terms are number

1. **State the problem:** Melvin wants to withdraw 65 from his bank account, which currently has 80. 2. **Identify the operation:** Withdrawing money means subtracting the amount w