🧮 algebra

1. **State the problem:** We need to show that the equation $$\frac{4}{x^2} = 3x + 7$$ can be rearranged to the form $$(x + 1)(x + 2)(3x - 2) = 0$$.

1. **Solve the inequality (i):** 4(x + 2) > 6 + 2x, where x \in \mathbb{R} Start by expanding and simplifying:

1. **State the problem:** Solve the cubic equation $$0 = 3x^3 + 7x^2 - 4$$ for $x$. 2. **Formula and approach:** There is no simple formula like the quadratic formula for cubic equ

1. **Problem 1:** Given the line $y = x$, find the $y$-coordinate when $x = -4$. 2. **Formula:** The equation of the line is $y = x$. This means for any value of $x$, $y$ is equal

1. **State the problem:** We are given multiple functions and a graph description of a line with a negative slope intersecting the y-axis at a positive value and the x-axis at a po

1. The problem is to convert the number .000005401 into standard form. 2. Standard form (also called scientific notation) expresses numbers as $a \times 10^n$ where $1 \leq |a| < 1

1. **Problem Statement:** We have a graph showing the relationship between the number of cellphones confiscated (x-axis) and the minutes of work done (y-axis). We need to analyze t

1. The problem is to identify and correct the error in the expression $$(2x - 7)^3 = (2x)^3 - 7^3 = 8x^3 - 343.$$ 2. The error is in the assumption that $$(a - b)^3 = a^3 - b^3.$$

1. **State the problem:** Simplify the expression $-5x^3 x - 2x^7$. 2. **Recall the rule for multiplying powers with the same base:** When multiplying terms with the same base, add

1. The problem states that the numbers must be above ten. 2. This means any number $x$ must satisfy the inequality $x > 10$.

1. The problem is to find numbers that satisfy a given identity. 2. First, identify the identity or equation you are working with. For example, if the identity is $a^2 - b^2 = (a-b

1. The problem is to understand and simplify the algebraic expression $3x + 4y - 7$. 2. An algebraic expression consists of variables, constants, and operations. Here, $3x$ and $4y

1. The problem asks for two numbers greater than ten that satisfy a certain condition, but the condition is not specified. 2. To provide a meaningful answer, please specify the con

1. **State the problem:** Prove the polynomial identity $$(a + b)(a - b) = a^2 - b^2$$. 2. **Recall the distributive property:** To multiply two binomials, multiply each term in th

1. **State the problem:** Simplify the expression $3 + i\frac{a}{b} - 1 - 6i$. 2. **Group like terms:** Combine the real parts and the imaginary parts separately.

1. **State the problem:** We want to determine if the equation $6x + 9 = hx + 15$ is solvable for $x$. 2. **Understand the equation:** This is a linear equation in $x$ with a param

1. **Problem:** Identify which graphs represent linear relations. **Explanation:** A linear relation is represented by a straight line on a graph. Curved lines or nonlinear shapes

1. Problem: Find the product $2a^3(3a + 5b)$. Formula: Use distributive property $x(y+z) = xy + xz$.

1. **State the problem:** We are analyzing a linear relationship between the number of cellphones confiscated (x) and the minutes of work done (y). 2. **Given data points:** (0, 3)

1. **State the problem:** Solve the inequality $$5 - 2x \geq -1$$ and determine which inequality symbol correctly represents the solution. 2. **Write the inequality:** $$5 - 2x \ge

1. The problem asks to identify the integer values that satisfy a certain inequality, but the inequality itself is not provided. 2. Since the inequality is missing, we cannot deter