🧮 algebra

1. **State the problem:** Determine if 8 and 21 are solutions to the equation $3x = 24$. 2. **Recall the equation:** $3x = 24$ means multiply $x$ by 3 to get 24.

1. The problem is to identify the equation corresponding to a graph that shows a sinusoidal wave with decreasing amplitude as $|x|$ increases, oscillating around $y=0$ with a perio

1. **State the problems:** We need to express and graph the piecewise functions:

1. **State the problem:** Solve the equation $$10x = 2.5x$$ and determine how many solutions it has. 2. **Write the equation:** $$10x = 2.5x$$

1. **State the problem:** We want to understand how to determine if an equation has no solution or infinitely many solutions. 2. **Recall the types of solutions for linear equation

1. The problem is to graph the linear equations: $$y = -\frac{1}{3}x - 3$$

1. The problem is to graph the linear equation $$y = -\frac{1}{3}x - 3$$. 2. The formula for a linear equation in slope-intercept form is $$y = mx + b$$, where $m$ is the slope and

1. **State the problem:** Determine whether the two expressions $$\frac{3x^3}{2}$$ and $$\frac{6x^4}{4}$$ are equivalent. 2. **Recall the rule for equivalence:** Two expressions ar

1. **State the problem:** We are given the function $$f(x) = \frac{3x^2 - 14x - 5}{3x^3 - x - 2}$$ and need to analyze its domain, vertical asymptotes, and horizontal asymptote.

1. **State the problem:** We are given six equations representing times $t$ when two vehicles meet. We need to sort these equations based on how often the vehicles meet: always, on

1. **State the problem:** We need to find the time $t$ when the blue car and the purple truck are at the same position on the road. The positions are given by the expressions $18t

1. The problem asks to describe the function representing the number of flyers Joaquin hands out over time based on the graph. 2. From the graph, the function is linear, starting a

1. **State the problem:** Solve the equation $14t = 14t + 18$ for $t$. 2. **Rewrite the equation:**

1. The problem asks what the value of a function at $x=0$ represents in a given situation. 2. Generally, for a function $f(x)$, the value at $x=0$ is $f(0)$.

1. The problem asks to write algebraic expressions for given verbal phrases. 2. For "Sum of q and x": The sum means addition, so the expression is $q + x$.

1. Write the algebraic expression for the messaging problems. 2. For 5x + 9x + x, combine like terms: $$5x + 9x + x = (5 + 9 + 1)x = 15x$$

1. **State the problem:** We need to find the final price of a sno-cone machine originally priced at 139 after applying a 20% discount and then adding a 6.75% sales tax. 2. **Formu

1. **State the problem:** Determine if 1.82 is a rational number. 2. **Recall the definition:** A rational number is any number that can be expressed as a fraction \( \frac{p}{q} \

1. The problem asks to write algebraic expressions for given verbal phrases. 2. For each phrase, we translate the words into algebraic terms:

1. **State the problem:** We need to find all real solutions to the equation $f(x) = 0$ based on the graph of $y = f(x)$. 2. **Understanding the problem:** The solutions to $f(x) =

1. The problem asks to find $f(10)$ for the piecewise function defined as: $$f(x) = \begin{cases} -\frac{x}{2} + 7 & \text{if } x \leq 6 \\ x - 2 & \text{if } x > 6 \end{cases}$$