🧮 algebra

1. **State the problem:** Solve the equation $x - 5 = \frac{x + 8}{6}$ for $x$. 2. **Formula and rules:** To solve equations involving fractions, multiply both sides by the denomin

1. **State the problem:** Solve the equation $$\frac{4}{5} x + \frac{6}{7} = 7x + \frac{87}{4}$$ for $x$. 2. **Write down the equation:** $$\frac{4}{5} x + \frac{6}{7} = 7x + \frac

1. **State the problem:** Solve the equation $$\frac{4}{5} x + \frac{6}{7} = 7x + \frac{87}{4}$$ for $x$. 2. **Write down the equation:** $$\frac{4}{5} x + \frac{6}{7} = 7x + \frac

1. **State the problem:** Solve the equation $$x - 6 = \frac{x + 9}{6}$$ for $x$. 2. **Formula and rules:** To solve equations involving fractions, multiply both sides by the denom

1. **State the problem:** We have a rectangle with width $$2x$$ and height $$x+1$$. The artist wants to enlarge this piece so that the area is at most 40 square feet, keeping the p

1. **State the problem:** We need to rearrange the equation $$w = 5(2a + b) - 6$$ to make $a$ the subject. 2. **Expand the brackets:** Use the distributive property to expand the r

1. **State the problem:** Simplify the expression $$2(6+4(2\times5-7))$$. 2. **Apply the order of operations (PEMDAS):** Parentheses, Exponents, Multiplication and Division (left t

1. **State the problem:** Solve the equation $$e^{2x} - 6e^x + 5 = 0$$ for $x$. 2. **Rewrite the equation:** Let $u = e^x$. Then the equation becomes $$u^2 - 6u + 5 = 0$$.

1. **State the problem:** Simplify the expression $$(4x+2)(2x+1)$$. 2. **Formula used:** To multiply two binomials, use the distributive property (also known as FOIL method for bin

1. **State the problem:** Simplify the expression $$(6a+5)(a-2)+(a-4)(a-4)$$. 2. **Use the distributive property (FOIL) to expand each product:**

1. **Stating the problem:** We need to evaluate $\log_5(8)$, which means finding the exponent to which we raise $5$ to get $8$.

1. O problema pede para simplificar a expressão $$\left(\frac{x^4}{y}-xy^2\right):\frac{x^2\sqrt{x}-xy\sqrt{y}}{xy\sqrt{x}+y^2\sqrt{y}}$$ para $x>0$ e $y>0$. 2. A divisão entre exp

1. **State the problem:** Identify which of the given equations use the commutative law. 2. **Recall the commutative laws:**

1. Let's understand the problem: We want to determine if we can find a certain value or property without knowing the value of $n$. 2. Generally, in algebra or sequences, $n$ often

1. **State the problem:** We need to determine which function grows faster as $n$ becomes very large: $n^{10!}$ or $0.0000001^n$. 2. **Recall the functions:**

1. Let's explore some complex-looking equations that simplify to $69$. 2. Consider the equation $$\frac{\sqrt{4761} \times (3^3 - 2^3)}{5} = 69$$.

1. **State the problem:** We have a totally ordered set $S$ with $n=7$ elements, each element $s_k$ corresponds to the $k$-th successor of zero in Peano arithmetic, i.e., $s_k = k$

1. Masalani tushuntirish: Ikki gul bor, har bir bargida raqam yozilgan. Har bir gulda bitta yashirin barg bor. Gul barglaridagi raqamlar yig'indilari teng. 2. Belgilash: Yuqori o'n

1. Masalani bayon qilamiz: ikkita gul bor, har bir bargida raqam yozilgan. Bitta barg yashirilgan. Gul barglaridagi raqamlar yig'indisi teng. 2. Berilganlar: yuqori gul barglari: $

1. **State the problem:** We need to order the following values from least to greatest:

1. **State the problem:** Simplify the fraction $\frac{2838}{9284}$. 2. **Formula and rules:** To simplify a fraction, divide numerator and denominator by their greatest common div