🧮 algebra

1. **State the problem:** Solve the equation $2(m + 3) - 6 = 18$ for $m$. 2. **Use the distributive property:** Multiply 2 by each term inside the parentheses:

1. **Problem statement:** Given real numbers $x$ and $y$ such that $2 \leq x \leq 5$ and $-3 \leq y \leq 4$, find the bounds (range) for the expressions $x+y$, $x-y$, $xy$, and $y^

1. The problem asks: If $f$ is a decreasing function, what is the direction (increasing or decreasing) of the function $g = f \circ f$, which means $g(x) = f(f(x))$. 2. Recall that

1. **State the problem:** Factor the quadratic expression $$x^2 + 3\sqrt{3}x - 30$$. 2. **Recall the factoring formula:** For a quadratic $$ax^2 + bx + c$$, we look for two numbers

1. The problem asks to solve the equation $$2x^3 - 5x = 0$$ by drawing a suitable straight line. 2. First, rewrite the equation as:

1. **State the problem:** Solve for $x$ in the proportion $\frac{7x+1}{2x+3} = \frac{10}{3}$. 2. **Formula and rule:** When two ratios are equal, their cross products are equal. So

1. The problem states: If $23p = 390$, find $p$. 2. The formula to solve for $p$ is to isolate $p$ by dividing both sides of the equation by 23.

1. **Stating the problem:** Calculate the average score for each student based on their Test and Exam scores. 2. **Formula used:** The total score is the sum of Test and Exam score

1. Probleem: Lahendada avaldis $$\frac{x^2(x+3)-2(x+3)}{6xy^2-3xy^2} \div \frac{x^2-9}{3x^2y - x^2y}$$. 2. Kasutame jagamise asemel korrutamist pöördväärtusega: $$\frac{A}{B} \div

1. The user requested a simpler explanation. 2. Since no specific math problem was given, I will provide a simple explanation of a common algebra concept: solving linear equations.

1. **State the problem:** Simplify or factor the expression $10x^2 - 9$. 2. **Formula and rules:** This is a quadratic expression. We can try to factor it using the difference of s

1. The problem asks to evaluate the sum \( \sum_{i=1}^{\infty} \frac{1}{2i} \). 2. This is an infinite series where each term is \( \frac{1}{2i} \) starting from \( i=1 \) to infin

1. **State the problem:** Simplify and analyze the function $$y=\ln\left(\frac{e^x}{e^x - 2}\right)^3$$. 2. **Recall the logarithm power rule:** $$\ln(a^b) = b \ln(a)$$. Applying t

1. **State the problem:** Simplify the expression $3x -(2y-4x) +6y$. 2. **Recall the distributive property:** When you have a minus sign before parentheses, distribute the minus to

1. **Problem statement:** Find the cubic polynomial $p(x)$ given that when divided by $x$, the remainder is 1; when divided by $x-2$, the remainder is 9; when divided by $x+2$, the

1. **State the problem:** Simplify the expression $7y + 2y$. 2. **Formula and rules:** When adding like terms, add their coefficients and keep the variable part the same.

1. **State the problem:** Add the two expressions $2x - 7y + 8z$ and $3x + 2y$. 2. **Write the expressions:**

1. **State the problem:** We want to multiply $9(7w + 8x)$ using the area model. 2. **Formula and rule:** The distributive property states that $a(b + c) = ab + ac$. Here, $a=9$, $

1. **State the problem:** We are given a proportion: $3\sqrt{3}$ is to 9 as $9\sqrt{2}$ is to some unknown number $x$. We need to find $x$. 2. **Write the proportion:**

1. **Problem:** Find the value of $n$ if the number of terms in the expansion of $(1 - 4x + 4x^2)^n$ is 7. 2. **Formula:** The number of terms in the expansion of a trinomial $(a +

1. The problem is to multiply $9(7w + 8x)$ using the area model. 2. The area model breaks the expression into parts: multiply $9$ by each term inside the parentheses separately.