🧮 algebra

1. **State the problem:** We need to graph the linear equation $$3x + y = 9$$. 2. **Rewrite the equation in slope-intercept form:** To graph easily, solve for $y$:

1. **State the problem:** We need to graph the equation $$3x + y = 9$$. 2. **Rewrite the equation in slope-intercept form:** To graph easily, solve for $y$:

1. **State the problem:** We are given the equation $$\frac{107\pi}{80} = \frac{201}{25} \theta$$ and need to solve for $\theta$. We also have $$\frac{\square}{3216} = \theta$$ and

1. **State the problem:** Solve the double inequality $$-6.5 \leq \frac{7x + 6}{2} \leq 20.5$$ and find any three solutions. 2. **Write the inequality:**

1. **Problem:** Determine how many small, medium, and large iced coffees were sold given prices and total sales. 2. **Define variables:**

1. **Problem:** A coffee truck owner sells small, medium, and large iced coffees at prices $5.50$, $6.75$, and $7.50$ respectively. They sold $95$ items totaling $628$. The number

1. **State the problem:** Find the equation of the line passing through points $(-2, 10)$ and $(6, 4)$ in the form $ax + by = c$ with integers $a$, $b$, and $c$ in lowest terms. 2.

1. **State the problem:** We are given the equation of line $l_1$ as $$x - 5y - 30 = 0$$ and a point $A(4,6)$ through which a line $l_2$ parallel to $l_1$ passes. We need to find t

1. **Problem Statement:** Determine if each given function is a polynomial function. If yes, write it in standard form, and identify the leading term, leading coefficient, and degr

1. **State the problem:** We are given a graph of a piecewise function and need to find:

1. **State the problem:** We need to find the domain, range, x-intercepts, y-intercept, and the missing function value $f(16)$ from the given graph. 2. **Domain:** The graph starts

1. **State the problem:** We need to find the value of the function at $x=1$, i.e., $f(1)$, given the domain $[0,\infty)$ and the description of the graph. 2. **Analyze the graph d

1. **State the problem:** Solve the inequality $$x^2 - 11x + 24 \leq 0$$ algebraically. 2. **Identify the type of inequality:** This is a quadratic inequality of the form $$ax^2 +

1. **State the problem:** Solve the inequality $$x^2 + 11x + 28 > 0$$ algebraically. 2. **Recall the formula:** This is a quadratic inequality. We first find the roots of the quadr

1. **Problem 1: Express the interval shown on the number line in interval notation.** The number line shows a green ray extending leftward toward negative infinity with a closed gr

1. **State the problem:** We need to express the interval shown on the number line in interval notation. 2. **Analyze the number line:** There is an open circle at $1$, which means

1. **State the problem:** We are given the formula for the area of a triangle $$A=\frac{1}{2}bh$$ and asked to solve for the base $$b$$. 2. **Write the formula:** $$A=\frac{1}{2}bh

1. **State the problem:** We need to solve the linear equation $$Ax + By = C$$ for the variable $$y$$. 2. **Isolate the term with $$y$$:** Subtract $$Ax$$ from both sides to get:

1. **State the problem:** Solve the inequality $$-18 + 3x \leq 0$$. 2. **Isolate the variable term:** Add 18 to both sides:

1. **State the problem:** Solve the inequality $$7x + 19 \geq 12$$. 2. **Write the inequality:** $$7x + 19 \geq 12$$.

1. **State the problem:** We need to determine which of the values $-1$, $9$, and $1$ satisfy the inequality $$5x - 10 \leq -5.$$ 2. **Rewrite the inequality:** $$5x - 10 \leq -5.$