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When solving equations, one of the primary goals is to find the value of the variable. To do this, we need to **isolate** the variable on one side of the equation. In our example, we have the equation \( 10x = 110 \). Here, \( x \) is the variable we want to isolate.
To achieve this, we need to undo any operations that are performed on \( x \). In this case, \( x \) is being multiplied by 10. To isolate \( x \), we will perform the opposite operation, which is division. By dividing the entire equation by 10, we effectively "move" the 10 away from \( x \), making \( x \) stand alone on one side.
Isolating the variable is like uncovering a gem hidden under layers; you need to remove everything hiding it first. Once isolated, you can then find its value with ease.

Balancing equations is a vital concept in algebra. An equation is like a seesaw; you need to maintain balance to make sure what you do on one side is mirrored on the other. In mathematical terms, this means that any operations we perform on one side of an equation, we must also perform on the other side.
In our example, \( 10x = 110 \), we divide both sides by 10 to isolate \( x \). By dividing the left side, we make \( x \) simpler, and by dividing the right side by the same number (10), we maintain the balance. This ensures the equation stays true and reflects the correct relationship between two sides.
Think of balancing equations as an essential strategy to maintain fairness. It helps you keep the equation valid while you manipulate it to solve for the variable.

Division is a fundamental operation in algebra that helps simplify equations and isolate variables. In our equation \( 10x = 110 \), the variable \( x \) is multiplied by 10. To solve for \( x \), we use division to remove the 10.
By dividing both sides of the equation by 10, using \( \frac{10x}{10} = \frac{110}{10} \), we essentially cancel out the 10 multiplying \( x \) on the left side. This leaves \( x \) alone, which is what we want to solve the equation. On the right side of the equation, we divide 110 by 10, giving us 11.
Division is a powerful tool because it helps break down complex or compounded relations in algebra. It can turn complicated expressions into simple, straightforward results for solving equations easily.