🧮 algebra

1. **State the problem:** We have a function $f(x) = -ax + b$ where $a$ and $b$ are constants.

1. **State the problem:** Write the equation $$5q^2 - 2q = 4q^2 - 6q + 45$$ in standard form and solve for $q$. 2. **Write the equation in standard form:** Move all terms to one si

1. **State the problem:** Solve the quadratic equation $6q^2 - 4q = 5q^2 - 7q + 54$. 2. **Rewrite the equation in standard form:** Move all terms to one side by subtracting $5q^2 -

1. **State the problem:** Given the equation $$\sqrt{15} - 9x = 48$$, find the value of $$x$$. 2. **Rewrite the equation:** The problem states $$\sqrt{15} - 9x = 48$$. Note that $$

1. **State the problem:** Solve the equation $\frac{x}{2} + \frac{x}{3} = 9$ for $x$. 2. **Formula and rules:** To solve equations with fractions, find a common denominator to comb

1. **State the problem:** We need to graph three lines on the same coordinate grid and identify the shape they form. 2. **List the equations:**

1. **State the problem:** Solve the equation $\frac{X}{2} + \frac{X}{3} = 9$ for $X$. 2. **Formula and rules:** To solve equations with fractions, find a common denominator to comb

1. **State the problem:** We need to write an equation relating the total cost $C$ to the number of slices of pie $r$ eaten, given an admission fee and a per-slice cost.

1. The problem asks to write the intervals shown on the number line in interval notation. 2. The intervals given are:

1. **State the problem:** We need to write the intervals shown on the number line in interval notation. 2. **Analyze the graph:**

1. **State the problem:** Write a piecewise function for the absolute value of $x+3$. 2. **Recall the definition of absolute value:** For any expression $A$, the absolute value $|A

1. **State the problem:** Solve the equation $$\frac{6x}{x^2 - 9} = \frac{18}{x + 3}$$ for $x$. 2. **Recall the formula and rules:** The denominators are $x^2 - 9$ and $x + 3$. Not

1. **State the problem:** Find the sum of the polynomials $$\left(\frac{1}{2} x^3 + 3x^2 - \frac{1}{4}\right) + \left(-\frac{1}{3} x^2 - 2x + 1\right).$$ 2. **Write the expression:

1. **Problem 1:** Determine the number of fire extinguishers needed for a building with 135,000 square feet, given that one extinguisher is needed for every 6,000 square feet. 2. *

1. **State the problem:** Luis needs to find the equation for the total cost $y$ to pour a concrete slab with area $x$ square feet, given an initial cost of 75 and an additional 2.

1. **State the problem:** Mr. Scarpa stays in a hotel that costs 78 per night. We need to write an equation for the total cost $c$ based on the number of nights $h$.

1. **State the problem:** We want to find the expression for the area of a large rectangle with dimensions $2x - 2$ (top side) and $x + 1$ (left side), from which a smaller rectang

1. The problem asks to complete statements about quadratic vocabulary. 2. The standard form of a quadratic equation is given by the formula:

1. **Problem Statement:** Find the axis of symmetry and vertex for the quadratic equation $y = x^2 + 6x + 4$. 2. **Formula for axis of symmetry:** The axis of symmetry for a quadra

1. **State the problem:** We have two rectangles: an outer rectangle with sides $5x + 8$ and $6x + 2$, and an inner rectangle with sides $x + 5$ and $3x$. The shaded region is the

1. **State the problem:** Solve the equation $$\frac{1}{x} = \frac{1}{5x} - \frac{x+3}{x^2}$$ for $x$. 2. **Identify the common denominator:** The denominators are $x$, $5x$, and $