🧮 algebra

1. **State the problem:** Solve the equation $$\frac{50}{x} + 7 = 107$$ for $x$. 2. **Isolate the fraction:** Subtract 7 from both sides to get $$\frac{50}{x} = 107 - 7$$

**Problem:** Let's factor the expression $x^2$! 🎉 1. **Imagine you have a box with $x^2$ blocks!** 📦

1. **State the problem:** Simplify the expression $$\frac{\left(\frac{2}{7}\right)^{-2}}{\left(\frac{7}{2}\right)^2}$$. 2. **Recall the rules:**

1. Problem: Simplify each expression with positive exponents only and evaluate when possible. 2. a) Simplify $ (5^{-3} \times 5^{9})(5^{3}) $.

1. The problem is to simplify the expression involving the natural logarithm and a linear term: $-2x - \ln(5)$. 2. The expression is already simplified as a sum of two terms: a lin

1. **State the problem:** Solve the equation $$\frac{\ln(-2x)}{5} - 5x = 0$$ for $x$. 2. **Rewrite the equation:** Multiply both sides by 5 to clear the denominator:

1. **State the problem:** Solve the equation $$\frac{1}{2} - \frac{n + 1}{5} = -\frac{1}{2}$$. 2. **Rewrite the equation:** To eliminate fractions, find the least common denominato

1. **State the problem:** Solve the quadratic equation $x^2 + 5x = 0$. 2. **Formula and rules:** To solve quadratic equations, one common method is factoring. If the equation can b

1. The problem is to solve the equation $2x + 3 = 7$ for $x$. 2. We use the basic algebraic principle of isolating the variable $x$ by performing inverse operations.

1. The problem is to add two formulas together. 2. The general formula for addition of two expressions is:

1. **State the problem:** Solve the equation $$\left(2+x\right)^2 + \left(\frac{20}{x} + 10\right)^2 = \left(40 \sqrt{x^2 + 10^2} + \sqrt{4 + \left(\frac{20}{x}\right)^2}\right)^2.

1. The problem: You want to know the most important SAT math formulas. 2. Key formulas to remember for SAT math include:

1. **State the problem:** We need to find which payment option is cheaper for a group of 10 students at an art gallery. 2. **Define the variables and expressions:** Let $n$ be the

1. The problem states that a phone plan costs 25 plus 0.10 per text. We need to write an expression for the total cost if $t$ texts are sent. 2. The formula for total cost $C$ when

1. The problem asks to solve the inequality $x > 20$. 2. This is a simple inequality where we want to find all values of $x$ that are greater than 20.

1. The problem is to understand the equation of a line given by $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept. 2. The formula $y = mx + b$ represents a straight li

1. **State the problem:** We need to find the equation of a line with slope $-\frac{1}{2}$ and y-intercept at the point $(0,3)$. 2. **Recall the formula:** The slope-intercept form

1. **State the problem:** Simplify the expression $\sqrt{\frac{25}{4} + 16}$.\n\n2. **Recall the formula:** The square root of a sum is not the sum of the square roots, so we first

1. Let's start by stating the problem: You want to understand how to "move" the numerator and denominator in fractions to isolate variables or expressions. 2. The key formula to re

1. The problem is about understanding how to manipulate fractions and move numerators and denominators across an equal sign in an equation. 2. When you have an equation like $$\fra

1. **State the problem:** Simplify the expression $4x - 14$. 2. **Identify common factors:** Both terms $4x$ and $14$ have a common factor of $2$.