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Understanding how to simplify algebraic equations is the first step to solving them. Simplification involves making the equation as straightforward as possible by removing complex fractions, combining like terms, and eliminating unnecessary elements. For instance, in our exercise,

we started with \(0.01(x+4)-0.04=0.01(5x+4)\). To simplify, the equation was multiplied by 100, which is a common technique to clear decimals and avoid small-number mistakes. This step transformed the equation into \(x+4-4=5x+4\), a much more approachable form. Remember, the goal is to make the equation easy to work with, without changing its truth value.

• Combine like terms: Add or subtract terms that have the same variable to a single side.
• Clear fractions: Multiply every term by a common denominator to remove fractions.
• Eliminate zeroes: If you have a term canceling itself out, like +4 and -4, remove them completely.

These actions don't just aid in solving; they also reduce the risk of errors in subsequent steps.

Solving for a variable requires isolating the variable on one side of the equation. After simplifying the equation, our next step was to get all the terms containing \(x\) on one side and the constant terms on the other. In the given problem, we subtracted \(x\) from both sides of the equation, which gave us \(4=4x\).

Following this, we divided both sides by 4, giving us the solution \(x=1\). Isolating the variable involves:

• Adding or subtracting terms from both sides to keep the equation balanced.
• Multiplying or dividing both sides by the same number to solve for the variable.
• Using inverse operations, such as using division to counteract multiplication, to simplify the variable's coefficient to 1.

Consistently applying these techniques will allow you to solve not only simple but also complex equations.

After solving an algebraic equation, it's crucial to verify the accuracy of your solution. The process involves substituting the variable with the found value back into the original equation to confirm that it results in a true statement. In our exercise, substituting \(x=1\) back into the original equation yielded \(0.01(1+4)-0.04=0.01(5 \times 1+4)\), which simplifies to \(0.05-0.04=0.09\), a true statement.

Through the verification step, we confirm that our solution makes the original equation hold true. Always double-check your solutions to ensure accuracy and strengthen your understanding. Here are some reasons why this step is important:

• It validates the solution and your understanding of the equation.
• It helps to catch and correct any arithmetic or algebraic mistakes.
• It provides a sense of assurance and confidence in your mathematical skills.

Never skip this final step, as it is an integral part of solving algebraic equations correctly.