Problem 96 - Introductory Algebra for College Students

Question

Explain how to clear decimals in a linear equation.

Step-by-Step Solution

Answer

The main concept for clearing decimals in a linear equation is to multiply each term by a suitable number (in many cases it might be 10, 100, 1000, etc) that converts all the decimals to integers. As an example, in the equation \(2.5x = 1.5\), multiplying by 10 cleared decimals to result in \(25x = 15\), which was then simplified to find \(x = 0.6\).

Step 1: Identify the Decimal

The initial stage of this process is to find the decimal or the fraction that needs to be cleared. It could be any number in the equation. Assume the equation as \(2.5x = 1.5\).

Step 2: Determine the Least Common Multiple

The next step is to find the least common multiple (LCM) or the least number which can turn the decimal into an integer by multiplication. Here, in order to get rid of the decimal, multiply everything by 10 because it's the lowest number that can convert 2.5 and 1.5 to integers.

Step 3: Apply Multiplication

Now, apply this multiplication to each term in the equation to remove the decimal points. So, multiplying everything by 10 gives the new equation as \(25x = 15\).

Step 4: Solve the equation

With the decimal cleared, the equation is much simpler to solve. Now, to find the value of x, divide both sides by 25. \(x = 15/25\), which simplifies to \(x = 0.6\).