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In linear equations, you often encounter constants on both sides of the equation. A constant is simply a number without any variables attached. In the example provided, the equation is given as12x - 8 = 64. Here, -8 and 64 are constants. To solve such equations, we need to isolate the variable by moving constants to one side of the equation.

So, we adjust the equation to remove the constant term on the variable side (left side in this case). We add or subtract the constant term from both sides, as seen in:

• 12x - 8 + 8 = 64 + 8

By performing this operation, we shift the constant term and simplify the process of isolating the variable.
This step ensures that the terms involving the variable are on one side, while constants are on the other side of the equation.

Isolating the variable is a critical step in solving linear equations. After moving constants to one side of the equation, our goal is to have our variable (in this example, x) by itself on one side of the equation. Following the previous example:

12x = 72

Here, the variable x needs to be isolated. This can be done by performing the opposite operation to whatever is attached to the variable. Since the variable x is multiplied by 12, we perform division on both sides of the equation to isolate x.

• 12x / 12 = 72 / 12

This simplifies to:

x = 6

This is known as isolating the variable. It helps us find the solution to the equation by making the variable stand alone on one side.

Linear equations are algebraic expressions that represent straight lines when graphed and have the form of ax + b = c. These equations involve variables raised to the power of one and can include constants.

To solve a linear equation, follow these essential steps:

• Perform operations to move constants to one side (as seen in the first section).
• Isolate the variable by performing inverse operations (as seen in the second section).
• Simplify the equation to its simplest form.

In our example, the linear equation 12x - 8 = 64 is solved by moving the constant -8 to the other side, simplifying it to 12x = 72, and then isolating x to get x = 6.
Remember, practice and familiarity with these steps will make solving linear equations easier over time.