🧮 algebra

1. The problem is to evaluate the logarithm of a fraction, specifically $\log \frac{2}{ }$. However, the denominator is missing, so the expression is incomplete. 2. The logarithm o

1. Problem: Löse die Gleichung $m + 5 = 11$ nach $m$ auf. 2. Formel: Um eine Variable zu isolieren, subtrahiere die Zahl auf der gleichen Seite wie die Variable von beiden Seiten d

1. **State the problem:** Solve the equation $$\frac{2x+4}{x-3} = 3$$ for $x$.

1. **Problem statement:** Alice wants to buy the same number of apples, oranges, and pears. Apples come in packs of 12, oranges in packs of 7, and pears in packs of 9. We need to f

1. **State the problem:** Solve the equation $$\frac{2x+4}{x-3} = 3$$ for $x$. 2. **Formula and rules:** To solve a rational equation, multiply both sides by the denominator to eli

1. **State the problem:** Solve the equation $2n + 6 = 14$ for $n$. 2. **Write down the equation:**

1. We are asked to express $x^2 + 4x + 1$ in the form $(x + a)^2 - b$ and then solve $x^2 + 4x + 1 = 0$. 2. To express $x^2 + 4x + 1$ in the form $(x + a)^2 - b$, we complete the s

1. **State the problem:** Simplify and verify the expression $$(\sqrt{3} + \sqrt{2})^2 - (\sqrt{3} - \sqrt{2})^2 = 4 \sqrt{6}$$. 2. **Recall the formula:** Use the difference of sq

1. **State the problem:** Simplify the expression $$(17^6)^5 \cdot (17^7)^{-8}$$ giving the answer with a positive exponent. 2. **Recall the exponent rules:**

1. **State the problem:** Simplify the expression $$\frac{a^3 \cdot a^{-5} \cdot b^{-4}}{(a \cdot a^{-4} \cdot b^2)^3}$$ so that all exponents are positive. 2. **Recall exponent ru

1. **State the problem:** Simplify the expression $$\frac{(m^{-1})^{-1} \cdot (m^2)^{-5}}{m^{-1} \cdot m^5}$$. 2. **Apply the power of a power rule:** $$(a^b)^c = a^{bc}$$.

1. **State the problem:** Simplify the expression $$\frac{(2c^6)(4c)}{8c^3}$$ and express the answer with positive exponents. 2. **Write the expression:** $$\frac{(2c^6)(4c)}{8c^3}

1. **State the problem:** Solve the quadratic equation $$5x^2 = 3 - x$$ and find the values of $x$ correct to 2 decimal places. 2. **Rewrite the equation:** Move all terms to one s

1. **State the problem:** Solve the quadratic equation $$2x^2 + 3x = 10$$ for $x$, with answers correct to 2 decimal places. 2. **Rewrite the equation:** Move all terms to one side

1. **State the problem:** Simplify the expression $-4(2x-5y)$. 2. **Formula and rule:** Use the distributive property: $a(b+c) = ab + ac$.

1. **State the problem:** Simplify the expression $-4(2x-5y)$. 2. **Formula and rule:** Use the distributive property: $a(b+c) = ab + ac$.

1. **State the problem:** An item is on sale for 45% of its original price. The original price is 35. 2. **Formula:** Sale price = Original price \times Percentage of original pric

1. **State the problem:** An item originally priced at 35 is on sale for 45% of the original price. We need to find the sale price. 2. **Formula used:** Sale price = Original price

1. **State the problem:** We know that 28,100 employees represent 18.2% of the total employees of the company. We need to find the total number of employees. 2. **Formula used:** T

1. **State the problem:** We need to find the minimum price for a dozen eggs if the total cost of four dozen eggs plus a half gallon of milk costing 2.97 exceeds 10.

1. **State the problem:** An automobile salesman makes 100 plus a 2% commission on the sale price of a car. We want to find the minimum sale price of a car so that the salesman mak