91Ó°ÊÓ

Solving equations can seem daunting at first, but it becomes manageable if you understand the basic principles behind it. The equation given \(-5x = -3x - 2\) asks you to find the value of \(x\) that makes both sides equal. An equation is like a balance scale; whatever you do to one side, you must do to the other to keep it balanced.The initial step when solving an equation is to get all the terms containing the variable (in this case \(x\)) on one side. This is accomplished by performing operations such as adding, subtracting, multiplying, or dividing both sides. By doing so, the equation becomes simpler to solve. In our example, we add \(3x\) to both sides to manage the variable terms.

Breaking down math problems into step-by-step solutions is a great way to simplify and understand the problem. Let's look at how this was done in our original solution.**Step 1: Eliminate Variable from One Side**We began by adding \(3x\) to each side of the equation \(-5x + 3x = -3x + 3x - 2\). This action eliminates \(x\) from the right side and simplifies to \(-2x = -2\). This key step is crucial as it reduces the complexity of the equation.**Step 2: Solve for x**Once we have the equation \(-2x = -2\), the next step is straightforward. By dividing both sides by \(-2\), we isolate the variable, yielding \(x = 1\). Following these steps ensures that each transition is logical and understandable, crucial for correctly solving any equation.

Prealgebra is all about building a strong mathematical foundation. In this exercise, a few core prealgebra concepts are at play:

• **Combining Like Terms:** When you add \(3x\) to \(-5x\), you're combining like terms—an essential skill in simplifying equations.
• **Equations as Balances:** Understanding that both sides of an equation should balance helps you comprehend why we add or subtract terms from both sides.
• **Inverse Operations:** When solving \(-2x = -2\), using the inverse operation (division) helps isolate \(x\). This principle applies to many math problems and aids in solving them efficiently.

These prealgebra skills ensure that, even in more complex equations, you have a reliable method to work towards a solution. Mastering these concepts makes tackling equations in algebra and beyond much less intimidating.