🧮 algebra

1. **State the problem:** Solve the equation $$\frac{2}{3} = \frac{3}{4} + \frac{2}{3}$$ for equality. 2. **Understand the problem:** We want to check if the left side equals the r

1. **State the problem:** Solve for $x$ in the equation $$\frac{2}{3} = \frac{x}{4}$$. 2. **Formula and rule:** To solve for $x$ in a proportion $\frac{a}{b} = \frac{c}{d}$, use cr

1. The problem is to solve a system of equations using the elimination method. 2. The elimination method involves adding or subtracting equations to eliminate one variable, making

1. **Problem statement:** There are two numbers. When the second number is subtracted from twice the first number, the result is 18. When 9 is added to the first number, the result

1. The problem is to multiply two numbers in scientific notation: $$(4.001 \times 10^{4}) \times (3.3 \times 10^{3})$$. 2. Recall the rule for multiplying numbers in scientific not

1. **State the problem:** Simplify the expression $$\frac{x^2 - 2cx + c^2}{x^2 - c^2}$$. 2. **Recognize the formulas:** The numerator is a perfect square trinomial and can be facto

1. Solve for $x$ in the equation $$\frac{-12\sigma^{12}}{x^{13}} + \frac{6\sigma^{6}}{x^{7}} = 0.$$ 2. Start by isolating terms: $$\frac{-12\sigma^{12}}{x^{13}} = -\frac{6\sigma^{6

1. **State the problem:** We need to complete the table of values for the functions $f(x) = 4^x - 3$ and $g(x) = 4x^2 + 2$ at $x = 1, 2, 3, 4$.

1. **State the problem:** Simplify the expression $$\frac{\sqrt{c+h}-\sqrt{c}}{h}$$ where $h \neq 0$. 2. **Recall the formula:** To simplify expressions involving differences of sq

1. The problem asks to classify a quadratic function as linear, nonlinear, or constant. 2. A quadratic function is generally of the form $$f(x) = ax^2 + bx + c$$ where $a \neq 0$.

1. **State the problem:** We analyze the graph of Michael Jordan's jump height $h$ as a function of time $t$. 2. **Identify the function type:** The graph is a parabola opening dow

1. **State the problem:** We need to complete the table of values for the functions $f(x) = 5x + 4$ and $g(x) = x^2 + 2x + 3$ at $x = 2, 3, 4, 5$.

1. **State the problem:** Simplify the expression $$\frac{x}{\sqrt{x^2 + y^2}} - \frac{1}{x^2 + y^2}$$. 2. **Identify the common denominator:** The terms have denominators $$\sqrt{

1. **State the problem:** John drives south 8 miles, then east 15 miles, and returns home via a straight road. We need to find the total distance he drives in 7 days. 2. **Use the

1. **Problem:** Simplify the expression $$\frac{1}{3 + \frac{2}{x}}$$. 2. **Formula and rules:** When simplifying complex fractions, combine terms by finding a common denominator o

1. **State the problem:** Simplify the expression $$\frac{2x^2 - 8}{4x}$$. 2. **Formula and rules:** To simplify a rational expression, factor the numerator and denominator and the

1. The problem is to graph the line given by the equation $$y = \frac{1}{5}x + 8$$ using the slope and y-intercept. 2. The slope-intercept form of a line is $$y = mx + b$$ where $m

1. **State the problem:** We are given that the temperature $y$ in degrees Fahrenheit is a linear function of the number of cricket chirps $x$. When $x=40$, $y=50$, and when $x=80$

1. **State the problem:** We are given two points on a linear function relating chirps per minute $x$ to temperature $y$: $(40, 50)$ and $(80, 60)$. The slope (rate of change) is $

1. **State the problem:** We are given two points on a linear function representing temperature $y$ in degrees Fahrenheit based on the number of cricket chirps $x$. The points are

1. **State the problem:** We need to check if $x=3$ is a solution to the equation $$5(x + 2) = 2x + 19$$ by substituting $x=3$ into both sides and verifying if they are equal. 2. *