🧮 algebra

1. **State the problem:** Solve the system of equations using Gaussian elimination: $$\begin{cases} 2x - y + 3z = 15 \\ x + 2y - 2z = -12 \\ 2x - 3y - 4z = 2 \end{cases}$$

1. **State the problem:** Solve the equation $$4\left(\frac{x}{6} + 5\right) = 2x + 10$$ for $x$. 2. **Use the distributive property:** Multiply 4 by each term inside the parenthes

1. Let's understand how signs change in algebraic expressions. 2. When you multiply or divide by a negative number, the sign of the term changes: a positive becomes negative, and a

1. The problem asks to identify the values of $x$ and $y$ for questions numbered 19, 20, and 21. 2. Since no specific equations or contexts are provided for these questions, we can

1. **Problem Statement:** We need to find the time when the temperature first reached 67°F based on the given temperature vs. time graph. 2. **Understanding the Graph:** The temper

1. **Problem Statement:** We are given a graph showing the inches of snow on the ground over time during a snowstorm. The snow falls at a constant rate for some hours, then stops,

1. **Problem Statement:** We need to find after how many minutes Indigo was 3 blocks from her house based on the given distance-time graph. 2. **Understanding the Graph:** The grap

1. **Problem Statement:** We need to match the correct graph to the story of a plumber charging a fixed fee plus a fixed amount per hour. 2. **Understanding the problem:** The tota

1. **Stating the problem:** Simplify the expression $-\left(2\left((1[x-1]1)\right)^2\right) + 5$. 2. **Interpreting the expression:** It seems the expression is $-\left(2(x-1)^2\r

1. **State the problem:** Simplify the expression $$3\left[\left(1[x+4]1\right)^2\right] - 7$$. 2. **Interpret the expression:** The notation is a bit unusual, but it seems to mean

1. **State the problem:** Simplify the expression $$\frac{x^4 - 2x^3 - x + 2}{x - 2}$$ by performing polynomial division. 2. **Recall the formula:** When dividing a polynomial $P(x

1. **State the problem:** Simplify the linear equation $$4a + b + 5 - 2c = 9 - 3c + 3a$$. 2. **Write down the equation:** $$4a + b + 5 - 2c = 9 - 3c + 3a$$.

1. **State the problem:** Simplify the expression $$5x^{-3} y^{2} \cdot (-2x^{-4} y^{-5})$$. 2. **Recall the rules:** When multiplying terms with the same base, add the exponents:

1. **State the problem:** Simplify the linear equation $$-12 - 4c - 16a = -6c - 19a + 2 + 2b$$. 2. **Rewrite the equation:** Move all terms to one side to combine like terms.

1. **Problem statement:** Express the sum or difference of logarithms as a single logarithm. 2. **Formula and rules:**

1. **State the problem:** We need to analyze and understand the function $$f(x) = 5 + \log_2 x$$. 2. **Recall the logarithm properties:** The logarithm $$\log_2 x$$ is defined only

1. **State the problem:** Simplify the expression $$\frac{n \times n + n}{n} = 10$$ and solve for $n$. 2. **Write the expression clearly:** The numerator is $n \times n + n = n^2 +

1. **Problem Statement:** We have the quadratic expression $4x^2 + bx - 45$, where $b$ is a constant. It can be factored as $(hx + k)(x + j)$, where $h$, $k$, and $j$ are integers.

1. **Stating the problem:** Factor the polynomial $$a^2 + 3b^2 + 4ab + 2ac + 6bc - 4b + 4c - 4$$ using $a$, $b$, or $c$ as the variable. 2. **Choosing variable $a$ to factor:** Gro

1. **Problem statement:** Factor the expression $$ab + 2ac + 3b^2 + 6bc - 5a - 13b + 4c - 10$$ 2. **Exercise (1) with variable $a$:**

1. **State the problem:** We are given the quadratic equation $$x^2 - 2x - 9 = 0$$ and told one solution can be written as $$1 + \sqrt{k}$$. We need to find the value of $$k$$. 2.