🧮 algebra

1. **State the problem:** Solve the quadratic equation $2x^2 - 2x = 112$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation equal to zero:

1. **State the problem:** Evaluate the expression $2+5(8-5)$.\n\n2. **Apply the order of operations (PEMDAS/BODMAS):** Parentheses first, then multiplication, then addition.\n\n3.

1. **State the problem:** Simplify the equation $$-

1. The problem asks us to solve the equation using the Zero-Product Property: $$(3x - 7)(2x + 1) = 0$$ 2. The Zero-Product Property states that if the product of two factors is zer

1. **State the problem:** Solve the equation $ (x + 7)(4x - 5) = 0 $ using the Zero-Product Property. 2. **Recall the Zero-Product Property:** If the product of two factors is zero

1. **State the problem:** Solve the inequality $3 + y > 9$. 2. **Isolate the variable:** To solve for $y$, subtract 3 from both sides:

1. **Problem:** Determine if 64 is both a power of 2 and a power of 4. 2. **Recall:** A number $a$ is a power of $b$ if $a = b^n$ for some integer $n$.

1. **Problem statement:** Given the polynomial $x^2 + 4x + 2a$, its zeroes are $a$ and $\frac{2}{a}$. We need to find the value of $a$. 2. **Formula used:** For a quadratic polynom

1. **State the problem:** A gas barbecue has a series of discounts: $420 less, 33.3\%, 20\%, and 5\%$ off the original price. Then, it is marked up by 60\% of the regular selling p

1. **State the problem:** Solve the system by substitution: $$y = 7x - 22$$

1. **Stating the problem:** Solve question 2 related to sales, cost, markup, markdown, or profit/loss calculations involving percentages. 2. **Identify the problem:** Since the use

1. **State the problem:** Solve the inequality $$-5 < 1 + \frac{3}{2}(-4x + 6)$$ for $x$. 2. **Recall the distributive property:** Multiply $\frac{3}{2}$ by each term inside the pa

1. **State the problem:** Solve the quadratic equation $$3x^2 + 3x - 6 = 0$$. 2. **Formula used:** The quadratic formula is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a$, $b

1. **Problem statement:** Given functions $f(x) = 3x + 5$ and $g(x) = x^2 - 2$, perform the following operations: a) $f(x) + g(x)$

1. **State the problem:** Solve the inequality $$-4 + 4(4r - 8) \leq 10r - 9 - 6$$ for $r$ and write the answer in simplest form. 2. **Apply the distributive property:** Multiply 4

1. **Problem 1: Calculate the total cost of a meal including tax** The meal costs $45 and the tax rate is 8%. We want to find the total cost including tax.

1. **State the problem:** Solve the inequality $$5 + 2(6b - 10) > -b + 8 - 7$$ for $b$ and write the answer in simplest form. 2. **Expand and simplify both sides:**

1. **State the problem:** Solve the inequality $$9 + 3(-3t + 10) \leq 6t + 8 - 4$$ for $t$ and write the answer in simplest form. 2. **Apply the distributive property:** Multiply $

1. Stating the problem: Solve the system of linear equations: $$-5 + 3x = 16$$

1. **Stating the problem:** We want to understand and solve the equation $$\frac{\sqrt{2}}{2} = \frac{2x + 9}{\sqrt{x^2 + 74.3}}$$ and the equivalent transformations given. 2. **Or

1. **Problem statement:** The line $l$ passes through the point $(4, 2)$ and forms a triangle with the coordinate axes with area 25 square units. The line cuts the x-axis at $(x_1,