91Ó°ÊÓ

Solving equations involves finding values for variables that make the equation true. In simpler terms, it's like solving a puzzle where each piece fits a particular spot. At the core of solving equations is the need to maintain balance. If you make a change on one side of the equation, you must do the same to the other side to keep everything in harmony.
Let's consider the equation given: \(5x + 2 = 32\). It's like a balanced scale. Each side must weigh the same for the scale to stay even. To solve this puzzle, we want to figure out what \(x\) needs to be to make both sides equal. We'll use mathematical operations to do this, such as addition, subtraction, multiplication, and division.

• Remember: whatever operation you perform on one side, do it to the other!
• Think of equations as balances. Keep them equal!

Isolating the variable means getting the letter (variable) by itself on one side of the equation. Imagine your equation is a sticky note on a board and the variable is the main point. Your task is to clear away all the clutter around it, leaving it in the spotlight.
Looking at \(5x + 2 = 32\), our goal is to isolate \(x\). We start by removing the constant number 2 using subtraction. Subtract 2 from both sides of the equation: \[5x + 2 - 2 = 32 - 2\].
This simplifies to \(5x = 30\). Now, \(x\) is the main focus but it still has a 5 clinging to it in the form of multiplication.
Next, divide both sides by 5 to isolate \(x\). This action gets us \(x = 6\). When the variable stands alone, you've completed isolation!

• Clear away constants first with addition/subtraction.
• Isolate the variable fully using multiplication/division.

Algebra involves following systematic steps to solve problems efficiently and correctly. Each problem may slightly vary, but following the right sequence is the key to getting it right.
In our equation \(5x + 2 = 32\), we can break down our process into simple steps:1. **Identify the equation and any constants or coefficients** that surround the variable. Here, we see \(5x\) and the constant 2.2. **Clear any constants** using addition or subtraction. Subtract 2 from both sides to get \(5x = 30\).3. **Eliminate coefficients** using multiplication or division. Divide both sides by 5 to simplify to \(x = 6\).
These steps keep everything organized, so you'll always know what to do next. With practice, these will become second nature.

• Follow steps: constants first, coefficients second.
• Keep your work neat; each step on a new line.