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The process of solving for x refers to finding the value of the variable x that makes the equation true. When you come across an equation like \(\frac{x}{4} = -6\), it's like solving a mystery. Start by looking at the equation as a balance scale where both sides are equal. To maintain this balance, whatever you do to one side of the equation, you must also do to the other side. This way, you'll uncover the value that x holds.

In the example given, the variable x is divided by 4. To free x and solve for its value, you need to undo the division. This is where multiplication comes into play. You multiply both sides of the equation by the same number that x is divided by, which is 4. Therefore, by multiplying \(\frac{x}{4}\) by 4, you're left with x on one side, and by multiplying -6 by 4, you get the value of x, which is -24. This is the essence of solving for x - balancing the equation to find that hidden number.

To isolate the variable means to get the variable on one side of the equation all by itself. Think of it as clearing out a room until only the desired individual, in this case, x, remains. This is a fundamental goal in solving algebraic equations and it involves performing operations that reverse whatever is being done to the variable.

Look at the equation \(\frac{x}{4} = -6\). The variable x is currently 'trapped' in a fraction. Your job is to free it. Multiply both sides by 4 and you'll

The term algebraic manipulation encompasses the variety of mathematical operations you can perform to rearrange and solve equations. It's like using a toolkit to remodel a room so that you can clearly see all its features. In algebra, the tools are adding, subtracting, multiplying, and dividing, as well as applying the distributive property and combining like terms.

Through algebraic manipulation, an equation can be transformed step by step until the variable stands alone, as seen with the equation \(\frac{x}{4} = -6\).