🧮 algebra

1. **State the problem:** Simplify the expression $$\left(3w^3 \times w^4\right)^3$$. 2. **Recall the rules:**

1. **State the problem:** Solve the inequality $$8x - 6 \geq 10$$. 2. **Use the inequality rules:** To isolate $$x$$, add 6 to both sides:

1. **State the problem:** Solve the equation $x^2 = 1$ for $x$. 2. **Formula and rules:** The equation is a quadratic equation in the form $x^2 = a$. To solve for $x$, take the squ

1. The problem is to understand how $5b + 4b$ could become $3b^2$. 2. First, let's look at the original expression: $5b + 4b$.

1. **Problem statement:** We are given the rational function $$y = \frac{5 + x}{2 - x}$$ and its equivalent form $$y = \frac{x + 5}{-x + 2}$$. 2. **Goal:** Understand why these two

1. **Problem statement:** We are given the function $$y = \frac{x+5}{-x+2}$$ and asked to analyze or simplify it. 2. **Rewrite the function:** Notice that $$-x+2$$ can be rewritten

1. **State the problem:**\nWe are given the equation $$x - 4x - 1 = -3x - 2 + 1$$ and asked to identify any errors and solve it correctly.\n\n2. **Simplify both sides:**\nLeft side

1. **State the problem:** We are given the equation $$\frac{2}{3} x + 7 \frac{5}{6} = \frac{1}{2} x + 9$$ and a series of steps attempting to solve for $$x$$. We need to identify e

1. **Problem Statement:** We have two problems:

1. **State the problem:** We are given Dan's jogging data from a graph point $(10, 90)$, meaning Dan jogged 90 miles in 10 hours.

1. The problem is to understand the behavior and graph of the function $$f(x) = b^x$$ where $$0 < b < 1$$. 2. The formula for an exponential function is $$f(x) = b^x$$ where $$b$$

1. **State the problem:** Solve the equation $$2(x + 7) = -4x + 14$$ for $$x$$. 2. **Write the formula and rules:** Use the distributive property to expand expressions and then com

1. **State the problem:** We have a function $y = f(x)$ with a point $A(-2, 2)$ on its graph.

1. **State the problem:** Simplify the expression $$\frac{2x^4y}{3x^2} \cdot \frac{4xy^3}{2x^3y^2}$$. 2. **Rewrite the expression:**

1. **State the problem:** Simplify the expression $$\frac{2x^4y}{3x^2} \cdot \frac{4xy^3}{2x^3y^2}$$. 2. **Write the formula and rules:** When multiplying fractions, multiply the n

1. **Planteamiento del problema:** Tenemos la ecuación $$z + 7 = 21$$ y queremos encontrar el valor correcto de $z$. 2. **Fórmula y regla importante:** Para despejar $z$ en una ecu

1. **State the problem:** Find the answers to the questions shown in the exam paper. 2. **Question 1**

1. **Write as a power of 2:** a. $\sqrt[4]{8}$

1. **Problem Statement:** Understand what a square root is and how to work with it. 2. **Definition:** The square root of a number $x$ is a value $y$ such that $$y^2 = x$$.

1. **State the problem:** We are given a function $f(x) = 3x$ and asked to find a function $g(x)$ that represents the graph of $f$ translated 5 units up. 2. **Recall the translatio

1. **State the problem:** We start with the function $f(x) = |x|$ and want to find a function $g(x)$ that represents a reflection of $f(x)$ in the x-axis and a vertical stretch by