1) Combine like terms on each side of the equation. For example, write 3 instead of \( 1+ \) 1.

Certainly! Combining like terms is a fundamental step in simplifying and solving equations. **Like terms** are terms that have the same variable raised to the same power. Here's how you can combine like terms on each side of an equation, along with an example to illustrate the process. ### **Step 1: Combine Like Terms on Each Side of the Equation** **Example Equation:** \[ 2x + 3 + x - 5 = 4x - 2 + 6 \] Let's break down the process: 1. **Identify Like Terms on Each Side:** - **Left Side (\(2x + 3 + x - 5\)):** - **\(2x\)** and **\(x\)** are like terms because they both have the variable \(x\). - **\(3\)** and **\(-5\)** are like terms because they are both constants (numbers without variables). - **Right Side (\(4x - 2 + 6\)):** - **\(4x\)** is a single term. - **\(-2\)** and **\(6\)** are like terms because they are both constants. 2. **Combine the Like Terms:** - **Left Side:** \[ 2x + x = (2 + 1)x = 3x \] \[ 3 - 5 = -2 \] So, the left side simplifies to: \[ 3x - 2 \] - **Right Side:** \[ -2 + 6 = 4 \] So, the right side simplifies to: \[ 4x + 4 \] 3. **Write the Simplified Equation:** \[ 3x - 2 = 4x + 4 \] Now, the equation \(2x + 3 + x - 5 = 4x - 2 + 6\) has been simplified by combining like terms on each side to become \(3x - 2 = 4x + 4\). ### **Key Points to Remember:** - **Combine like terms only.** Unlike terms (terms with different variables or different exponents) cannot be combined. - **Add or subtract the coefficients (the numerical part) of like terms.** - **Keep constants (numbers without variables) separate from variable terms unless they are like terms.** ### **Another Quick Example:** Simplify the equation by combining like terms: \[ 5y + 2 - 3y + 7 = y - 4 + 9 \] **Solution:** - **Left Side:** \[ 5y - 3y = 2y \] \[ 2 + 7 = 9 \] So, left side becomes \(2y + 9\). - **Right Side:** \[ -4 + 9 = 5 \] So, right side becomes \(y + 5\). **Simplified Equation:** \[ 2y + 9 = y + 5 \] Now, you can proceed to solve for \(y\) by further simplifying the equation. --- By consistently applying the process of combining like terms, you can simplify complex equations and make them easier to solve. If you have a specific equation you'd like help with, feel free to share it!