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In basic algebra, isolating the variable is a key concept you need to understand. When solving equations, isolating the variable means getting the variable by itself on one side of the equation. Let's take the exercise example: \( j - 7.42 = -3.7 \) Here, our variable is \( j \). We need to manipulate the equation to isolate \( j \) on one side. We do this by performing the same operation on both sides of the equation. In this case, we add 7.42 to both sides: \( j - 7.42 + 7.42 = -3.7 + 7.42 \) This method ensures that we maintain the balance of the equation. Remember, whatever you do to one side of the equation, you must do to the other side as well. By isolating the variable, we can easily find its value.

Simplifying equations is another important concept in algebra. Once we've isolated the variable, the next step is to simplify both sides of the equation to find the solution. Let's continue with our example: After isolating the variable \( j \) as explained before, our equation looks like this: \( j - 7.42 + 7.42 = -3.7 + 7.42 \) Now, we need to simplify both sides: \( j = 3.72 \) By performing the addition and subtracting equal values, we reached the simplified form of the equation. Simplifying correctly ensures that the variable is alone on one side, and the other side gives the solution.

Understanding basic algebra is essential for solving equations efficiently. At its core, basic algebra involves some fundamental concepts:

• Identifying and isolating variables
• Performing arithmetic operations on equations
• Simplifying expressions

Using our solved example: \( j - 7.42 = -3.7 \) We begin by identifying our equation and the need to isolate the variable \( j \). Next, by adding 7.42 to both sides, we adjust the equation while maintaining its balance: \( j - 7.42 + 7.42 = -3.7 + 7.42 \) Finally, we simplify the expression to find: \( j = 3.72 \) These steps are the building blocks of basic algebra, helping you solve linear equations perfectly every time. Practice these techniques, and you'll be well on your way to mastering algebra!