🧮 algebra

1. **State the problem:** Solve the equation $$5^{-8}(2^x - 1)^3 = 125$$ for $x$. 2. **Rewrite constants:** Note that $125 = 5^3$, so the equation becomes $$5^{-8}(2^x - 1)^3 = 5^3

1. **State the problem:** Solve the equation $$3^{2x - 1} + 1 = 2$$ for $x$. 2. **Isolate the exponential term:** Subtract 1 from both sides:

1. The problem is to solve a quadratic equation by factoring instead of using the quadratic formula. 2. The general form of a quadratic equation is $ax^2 + bx + c = 0$.

1. The problem is to solve the quadratic equation $5x^2 - 11x + 6 = 0$. 2. We use the quadratic formula to find the roots of $ax^2 + bx + c = 0$:

1. **State the problem:** Find the coordinates of point C where line k crosses the x-axis.

1. The problem is to understand the formula for compound interest and how it relates to the given table. 2. The formula for compound interest is:

1. **State the problem:** We have three vegetable patches with areas $w$, $2w + 5$, and $4w$ respectively. The total area is greater than 61 $m^2$. We need to write and solve an in

1. **State the problem:** Samuel thinks of a number $k$. He triples it and then subtracts 11 to get a result less than 43. 2. **Write the inequality:** Tripling $k$ means $3k$. Sub

1. **Problem Statement:** Factor the expression $x^4 - 36$ using the difference of squares formula. 2. **Formula and Rules:** The difference of squares formula is $a^2 - b^2 = (a -

1. **State the problem:** Solve the quadratic equation $x^2 = 2x - 12$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. Stating the problem: Solve the equation $$\frac{4x}{1} \div 2 = x + 7$$. 2. Understand the division by 2: Dividing by 2 is the same as multiplying by $\frac{1}{2}$, so rewrite t

1. **State the problem:** Simplify the expression $$\frac{8}{12} \times x^{-3} \div t^2 \times t^3 \div x^2$$. 2. **Rewrite the expression:**

1. **State the problem:** Simplify the expression $$\frac{8}{12} \times \frac{x^3}{t^2} \times \frac{t^3}{x^2}$$. 2. **Write the expression clearly:**

1. Let's start by stating the problem: You want to understand the rules of logarithms. 2. The logarithm of a number answers the question: to what power must we raise a base number

1. **State the problem:** Factor the expression $$\frac{15x^2}{5xy} + \frac{25x^3}{3xy}$$. 2. **Rewrite each term:** Simplify each fraction by dividing numerator and denominator.

1. The problem is to find two phrases for the expression, which likely means rewriting or interpreting the expression in two different ways. 2. Since the user did not provide a spe

1. **State the problem:** Expand and simplify the expressions: a) $ (x - 1)(x + 4) $

1. The problem is to simplify the expression $20 - n$. 2. This is a simple algebraic expression where $20$ is a constant and $n$ is a variable.

1. **State the problem:** Factor the greatest common factor (GCF) out of the expression $$-60a^3 + 54$$. 2. **Identify the GCF:** The coefficients are 60 and 54. The GCF of 60 and

1. **State the problem:** We have a pyramid with three bricks. The top brick's value is the sum of the two bottom bricks' values. 2. **Given:**

1. **Problem Statement:** Analyze the linear function passing through points $(-1,1)$, $(0,0)$, and $(2,5)$. 2. **Formula and Rules:** The equation of a line through two points $(x