🧮 algebra

1. **State the problem:** Solve the equation $$\frac{x - 4}{2022} + \frac{x - 3}{2023} + \frac{x - 2}{2024} = 3.$$\n\n2. **Formula and approach:** To solve this linear equation, we

1. **State the problem:** Solve the equation $$\frac{x - 4}{2022} + \frac{x - 3}{2023} + \frac{x - 2}{2024} - 3 = 3$$ for $x$. 2. **Rewrite the equation:** Move the constant term o

1. **Problem Statement:** A publishing company has a cost of Le 0.38 per copy and revenue of Le 0.35 per copy. Dealers get Le 0.3 of the revenue. Advertising revenue is 10% of deal

1. **Problem:** A company produces product X at a unit cost of 10. Fixed costs are 450000, and each unit sells for 25. How many units must be sold to make a positive profit of 5100

1. **Problem:** Show that the middle term in the expansion of $ (1+x)^{2n} $ is given by $$ \frac{1 \times 3 \times 5 \times \cdots \times (2n - 1)}{n!} x^n $$

1. **Problem:** Show that the middle term in the expansion of $ (1 + x)^{2n} $ is given by $$ \frac{1 \times 3 \times 5 \times \cdots \times (2n - 1) \times 2^n \times x^n}{n!} $$

1. **State the problem:** We need to find a possible whole number length of a race track that rounds to 300 km when rounded to the nearest 100 km and rounds to 250 km when rounded

1. **State the problem:** Harley needs to cut the grass on a rectangular field that is 100 meters long and 90 meters wide. She cuts grass at a rate of 30 square meters per minute.

1. **State the problem:** We need to find the value of $A$ given three balancing scales involving bananas, pears, lemons, and peas. 2. **Assign variables:** Let

1. **State the problem:** Simplify the expression $$\frac{(2a)^2}{4a}$$. 2. **Recall the formula and rules:** When raising a product to a power, apply the exponent to each factor:

1. **State the problem:** Simplify the expression $$\frac{3 + \sqrt{5} + \sqrt{44}}{2}$$. 2. **Recall the rules:** The square root of a product can be simplified as $$\sqrt{a \time

1. The problem is to understand the topic of Surds, which are irrational roots that cannot be simplified to remove the root. 2. A surd is an expression containing a root, such as $

1. **State the problem:** We are given the first four terms of a sequence: 19, 23, 27, 31. We need to find the formula for the nth term of this sequence. 2. **Identify the type of

1. **State the problem:** Convert the linear equation $2x + 5y = 7$ into slope-intercept form. 2. **Recall the slope-intercept form:** The slope-intercept form of a line is given b

1. **State the problem:** We want to find the weight of the elephant based on the given scales and relationships between animals. 2. **Define variables:** Let the weights be:

1. **State the problem:** We are given a pair of linear equations $5x + 7y = 1$ and $ax + by = 1$ which represent perpendicular lines. We need to determine which of the given pairs

1. **State the problem:** Calculate the value of $$(29.29 \times 10^8) - (19.77 \times 10^8)$$. 2. **Formula and rules:** When subtracting numbers with the same power of 10, subtra

1. The problem is to calculate the difference between two products: $29.29 \times 108$ and $19.77 \times 108$. 2. We use the distributive property of multiplication over subtractio

1. **State the problem:** Calculate the sum of $50.57 \times 10^3$ and $25.354 \times 10^3$. 2. **Formula and rules:** When adding numbers in scientific notation with the same powe

1. **State the problem:** Calculate the value of the expression $$25 + \frac{32}{(10-6) \times 4}$$. 2. **Identify the order of operations:** According to PEMDAS/BODMAS rules, we f

1. **State the problem:** Calculate the difference between $9.96 \times 10^9$ and $7.44 \times 10^9$. 2. **Formula and rules:** When subtracting numbers in scientific notation with