🧮 algebra

1. **State the problem:** We need to find the values of $v$ that satisfy the inequality $$3v \geq 75$$ and then write an equivalent inequality in terms of $v$. 2. **Write the inequ

1. **State the problem:** We need to find values of $$u$$ that satisfy the inequality $$2u \leq -1$$ and then write an equivalent inequality for $$u$$. 2. **Write the inequality:**

1. **State the problem:** We want to find all values of $k$ such that the inequality $-k < 7$ holds true. 2. **Rewrite the inequality:** Starting with

1. The problem asks us to find all values of $y$ from the given list that satisfy the inequality $y \leq -3$. 2. The inequality $y \leq -3$ means $y$ is less than or equal to $-3$.

1. **State the problem:** Identify the property used in each step of solving the equation $2(5x - 7) = 2x + 10$. 2. **Step 1:** From $2(5x - 7) = 2x + 10$ to $10x - 14 = 2x + 10$

1. **Problem (a):** Simplify $\left(12 - \frac{2}{3}x + \frac{1}{2}x^2\right) - \left(x^3 + 3x^2 - \frac{1}{6}x\right)$. 2. **Step 1:** Distribute the minus sign to the second pare

1. **State the problem:** Simplify the expression $$72y^4 - 50x^4$$. 2. **Identify common factors:** Both terms have a common factor of 2.

1. **State the problem:**\nWe have a quartic function $f(x) = ax^4 - 2bx^2 + c$ defined on $[-2,2]$. We know $x-2$ and $2x+1$ are factors of $f(x)$, and the remainder when dividing

1. **State the problem:** We are given two equations: $$2x + 8y = 3$$ and $$x + 4y = 8$$ and values $$x = -24$$ and $$y = 26$$. We need to check if these values satisfy the equatio

1. **State the problem:** We need to rewrite the equation $$5x + 2y = 6$$ in slope-intercept form, which is $$y = mx + b$$ where $$m$$ is the slope and $$b$$ is the y-intercept. 2.

1. **State the problem:** We need to rewrite the equation $$4x + y = 1$$ in slope-intercept form, which is $$y = mx + b$$ where $$m$$ is the slope and $$b$$ is the y-intercept.\n\n

1. **State the problem:** We need to graph the linear equation $$y = 4x - 2$$ and identify its slope and y-intercept. 2. **Recall the slope-intercept form:** The equation of a line

1. **State the problem:** We are given the linear equation $$y = -2x + 5$$ and asked to complete a table of values for $x = -1, 0, 3$ and then graph the equation. 2. **Formula and

1. **State the problem:** We need to find the equation of a straight line that crosses the y-axis at $-3$ and the x-axis at about $-1.5$. 2. **Recall the slope-intercept form:** Th

1. The problem is to identify the graph of the linear equation $$y = -2x + 2$$. 2. This equation is in slope-intercept form $$y = mx + b$$, where $$m$$ is the slope and $$b$$ is th

1. The problem is to identify the graph of the linear equation $$y = -2.5x - 3$$. 2. The equation is in slope-intercept form $$y = mx + b$$, where $$m$$ is the slope and $$b$$ is t

1. **State the problem:** Expand the logarithmic expression $$\ln\left(\frac{x^8}{\sqrt{x^2 - 36}}\right)$$ using the laws of logarithms, given that $x > 6$. 2. **Recall the logari

1. **State the problem:** We are given the graph of $y = f(x)$, which is a horizontal line segment at $y = 2$ from $x = -2$ to $x = 2$. We want to graph $g(x) = f(x) - 2$. 2. **Und

1. **State the problem:** We are given a function $y = f(x)$ and asked to graph $g(x) = f(x) - 2$ using the graph of $f(x)$. 2. **Understand the transformation:** The function $g(x

1. **State the problem:** We need to find the number of apples sold between February and April based on the graph showing the number of apples remaining each month. 2. **Read value

1. **State the problem:** We need to find how much data Miko used from week 2 to week 3 based on the graph data. 2. **Identify data usage values:** From the graph description: