🧮 algebra

1. **State the problem:** Simplify the expression $\frac{2}{800 + 98}$. 2. **Add the numbers in the denominator:**

1. The problem is to explain the letter \textbf{b} clearly in a mathematical context. 2. Usually, \textbf{b} represents a constant, coefficient, or variable depending on the equati

1. **State the problem:** We have two functions $f(x) = 5x + 7$ and $g(x) = 6 - 8x$. We want to find $h(x)$ where $h(x) = f(x) + g(x)$ and then evaluate $h(6)$. Also, find the valu

1. **State the problem:** Solve for $x$ in the equation $$\sqrt{x} + 4! + \sqrt{x} = 12.$$\n\n2. **Recall the factorial value:** $4! = 4 \times 3 \times 2 \times 1 = 24$.\n\n3. **R

1. Let's start with a simple algebraic equation: Solve for $x$ in the equation $$2x + 3 = 11$$. 2. The formula to solve linear equations is to isolate the variable on one side. We

1. **State the problem:** We need to solve the system of equations graphically: $$y = 2x - 5$$

1. The user requests the exact term or sequence to solve for a precise answer and table. 2. To provide a precise answer, we need a clear problem statement or formula defining the s

1. **Stating the problem:** You asked to solve for the term and add the table, but the exact expression or sequence is not provided. Please provide the specific term or sequence to

1. **State the problem:** Solve the equation or expression given by the user. Since no specific equation was provided, let's consider a general approach to solving algebraic equati

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} x_1 - 4x_2 - 2x_3 = 0 \\ 3x_1 + 5x_2 + 5x_3 = 4 \\ 2x_1 - 5x_2 + 2x_3 = 15 \end{cases}$$

1. **State the problem:** We need to graph the system of inequalities: $$y < 2x + 3$$

1. **State the problem:** We need to determine which points are solutions to the system defined by the shaded triangular region bounded by two lines and the x-axis.

1. **State the problem:** We are given two systems of inequalities: System 1:

1. **State the problem:** We have a system of two inequalities represented by shaded regions on a graph. We want to write the system and determine which points satisfy both inequal

1. The problem asks to write the system of inequalities for the region where the graph shows shading above both lines. 2. The first line is given by the equation $y = x + 3$ with a

1. **State the problem:** Write the system of inequalities that corresponds to the shaded region above the line $y = x$ and below the line $y = 2x - 2$. 2. **Identify the boundary

1. **State the problem:** Solve the radical equation $$20 - 3\sqrt{t} = \sqrt{t} - 4$$. 2. **Isolate the radical terms:** Move all terms involving $\sqrt{t}$ to one side and consta

1. **State the problem:** A projector creates a 30 cm wide image when it is 50 cm from the screen. We want to find the width of the image when the projector is moved back 20 cm, so

1. The problem is to find the y-intercept of a function, which is the point where the graph crosses the y-axis. 2. The y-intercept occurs when $x=0$.

1. **State the problem:** We are given the linear equation $y = -3x + 12$ and want to understand its properties. 2. **Formula and rules:** This is a linear function in slope-interc

1. **State the problem:** Simplify the expression $100m - 15(2m+1)(m+1)$. 2. **Recall the distributive property and multiplication of binomials:** To simplify, first expand the pro