🧮 algebra

1. **State the problem:** Simplify and verify the equality: $$\frac{3}{5} + \left( \frac{5}{3} - \frac{3}{6} \right) = \frac{8}{5} + \left( \frac{7}{3} - 3 \right)$$

1. The problem is to solve the given math question and provide the final answers. 2. Since the user did not specify a particular problem, I will demonstrate solving a common algebr

1. **State the problem:** Find the center and radius of a circle given its equation. 2. **General form of a circle's equation:**

1. **State the problem:** Solve the equation $x^2 + y^2 - 10x - 2y - 74 = 0$ for $y$ in terms of $x$ or identify the geometric shape it represents. 2. **Rewrite the equation:** Gro

1. **Problem 216:** Given that Newspaper A sells for $1.00 and Newspaper B sells for $1.25, let the number of copies sold of A be $x$ and of B be $y$. 2. The total number of newspa

1. **State the problem:** Simplify the expression $$\frac{4x^2 - 17x - 15}{2x - 1} \times (2x^2 - 7x + 3) + \frac{29 - 4x}{x^2 - 25}$$ as a single fraction in simplest form. 2. **F

1. The problem is to factor the quadratic expression $3x^2 - 16x - 12$ using the middle term break method. 2. The middle term break method involves finding two numbers that multipl

1. The problem is to understand the "middle term break" method, which is a technique used to factor quadratic expressions of the form $ax^2 + bx + c$. 2. The formula for a quadrati

1. **Stating the problem:** We are given fractions of students who had measles, chicken pox, and neither during one year in a school. We need to find the fraction of students who h

1. **State the problem:** Solve the system of equations by elimination: $$\begin{cases}-x - 8y - 6z = -4 \\ -9x - 9y = 90 \\ 3x - 2y - 7z = -97 \end{cases}$$

1. **Énoncé du problème :** Soit la matrice $A = \begin{pmatrix} 2 & 0 & 1 \\ 1 & 1 & 1 \\ -2 & 0 & -1 \end{pmatrix}$. Nous devons :

1. **State the problem:** Solve the system of equations by elimination: $$\begin{cases} 3x - 6y + 3z = -27 \\ -2x + y + 4z = 18 \\ -x - 4y + z = 9 \end{cases}$$

1. **State the problem:** Solve the system of equations by elimination: $$\begin{cases} 4x - 4y + 5z = -20 \\ -3x - 2y - 4z = 9 \\ 3x + 6y + 6z = 3 \end{cases}$$

1. ප්‍රශ්නය: සියලු n ∈ \mathbb{Z}^+ සදහා $\left(x + \frac{1}{x}\right)^n$ හි ද්විපිද ප්‍රධාරණය ලිවීමයි. 2. $\left(x + \frac{1}{x}\right)^n$ හි ද්විපිද ප්‍රධාරණය ලිවීම සඳහා බිනෝමියල

1. **State the problem:** Solve the system of equations by elimination: $$\begin{cases}-3x + 5y - 5z = 6 \\ 6x - 5y + 5z = 3 \\ 2x + 6y - 2z = 40 \end{cases}$$

1. **State the problem:** Solve for $x$ in the equation $$\frac{1}{x} - \frac{1}{x+1} = \frac{1}{x+4}.$$ 2. **Write the equation and find a common denominator:** The denominators a

1. **State the problem:** Solve the system of equations by elimination: $$\begin{cases} 5x + 4y + 2z = -37 \\ 4x + 3y - z = -26 \\ -2x + 5y - 6z = -13 \end{cases}$$

1. **State the problem:** Solve the system of equations by elimination: $$\begin{cases} x - 3y - 3z = -13 \\ 2x + 3y + 2z = 14 \\ 2y - 3z = -15 \end{cases}$$

1. **State the problem:** Solve the system of equations by elimination: $$\begin{cases}-x + 3y + 3z = 18 \\ -x + 3y + 2z = 16 \\ x - y + 2z = 6 \end{cases}$$

1. **Problem 221:** Find the value(s) of $x$ such that $\frac{1}{x} = \frac{1}{x+1} = \frac{1}{x+4}$. 2. **Step 1:** Since all three fractions are equal, set $\frac{1}{x} = \frac{1

1. **State the problem:** Solve the system of equations by elimination: $$\begin{cases}-2x + 2y - 3z = -18 \\ -2x - y + z = 6 \\ -x - 3y + 2z = 12 \end{cases}$$