🧮 algebra

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

1. **State the problem:** We are given the function $$f(-x) = \frac{4}{(-x)^2 + (-x) + 4}$$ and need to simplify it. 2. **Recall the rules:**

1. **State the problem:** Find the symmetry of the function $f(x) = \frac{x^2 - 4}{5 + x}$. 2. **Recall the rules for symmetry:**

1. **State the problem:** Simplify the expression $$\frac{3a^9 r^{-3}}{-4 (a^2)^{-1}}$$. 2. **Recall the rules:**

1. **State the problem:** Simplify the expression $$\frac{3b^{-9}}{(3b^{-4}c^{-3})^{-3}}$$. 2. **Recall the rules:**

1. **State the problem:** Solve the equation $$\frac{x - 5}{7} = 40$$. 2. **Formula and rules:** To solve for $x$, multiply both sides of the equation by 7 to eliminate the denomin

1. **State the problem:** Solve the equation $$\frac{w+7}{4} = \frac{w-5}{3}$$ for $w$. 2. **Formula and rules:** To solve equations with fractions, multiply both sides by the leas

1. **State the problem:** Find the x-intercept and y-intercept of the line given by the equation $$y = -5x - 5$$ without graphing. 2. **Recall definitions:**

1. **State the problem:** Simplify the expression $$(3^2)^{-2}$$. 2. **Recall the power of a power rule:** When raising a power to another power, multiply the exponents:

1. **State the problem:** Solve the system of equations by substitution: $$y = 2x - 13$$

1. **State the problem:** Evaluate the expression $$-(2a)^2 + 1 + 3$$ for $$a = 2$$. 2. **Write the expression:** $$-(2a)^2 + 1 + 3$$.

1. Stating the problem: Solve the first equation $12x = 120$ for $x$. 2. Formula and rules: To solve for $x$, divide both sides of the equation by the coefficient of $x$, which is

1. **State the problem:** Evaluate the expression $5 (y + 2) - 61$ for $y = 3$. 2. **Write the expression:**

1. **State the problem:** Simplify the expression $$6 \div 2 - \left(81 \div 3^2\right)$$. 2. **Recall order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplication and

1. The problem asks about the slope of vertical and horizontal lines. 2. The slope of a line is defined as the change in $y$ divided by the change in $x$, or $$m=\frac{\Delta y}{\D

1. The problem asks to find the value of the function $s(t) = -3t + 8$ at $t = -2$. 2. The formula to evaluate a function at a given input is to substitute the input value into the

1. **Problem Statement:** Determine the domain and range of the graph described, which starts near (-3, -2), crosses the x-axis near (1,0), and ends at (4, 2). 2. **Understanding D

1. **State the problem:** We are given two sets of points and need to find the equations of the lines they represent. 2. **Identify the points:**

1. **State the problem:** Find the equation of the line passing through the points $(-2,3)$ and $(-1,1)$ in slope-intercept form $y=mx+b$. 2. **Find the slope $m$:** Use the formul

1. **State the problem:** Rose needs 200 litres of water to make 5 litres of iced tea. We want to find out how much water she needs to make 300 ml (which is 0.3 litres) of iced tea

1. **State the problem:** Find the equation of the line passing through points (0, 4) and (4, 2) in slope-intercept form $y=mx+b$. 2. **Formula:** The slope $m$ is given by $$m=\fr