Equations involving fractions can be intimidating, but with a step-by-step approach, they can be easily solved. In this guide, we will break down the process of solving equations with fractions, ensuring you have a clear understanding of each step along the way.

Step 1: Clear the Equation of Fractions

Before we can begin solving the equation, it is important to get rid of the fractions. Multiply the entire equation by a common denominator that eliminates all the fractions. This will make the equation easier to work with.

Step 2: Simplify the Equation

Once the fractions are cleared, simplify the equation by combining like terms if possible. This will help reduce the complexity of the equation and bring it closer to a solution.

Step 3: Solve for the Variable

Now that the equation is simplified, we can focus on isolating the variable. Perform the necessary operations to isolate the variable on one side of the equation while keeping the equation balanced. Remember to perform the same operation on both sides to maintain equality.

Step 4: Check Your Solution

After solving for the variable, it is important to check if the solution is valid. Substitute the obtained value back into the original equation and simplify both sides. If the equation still holds true, then the solution is correct. If not, retrace your steps and double-check your calculations.

Example:

Let’s go through a sample equation to see these steps in action:

2/3(x + 1) – 1/4(2x – 5) = 1/2

Step 1: Clear the Equation of Fractions

  • Find the common denominator: 3 * 4 = 12
  • Multiply all terms by 12 to get rid of fractions

The equation becomes: 8(x + 1) – 3(2x – 5) = 6

Step 2: Simplify the Equation

  • Distribute the terms: 8x + 8 – 6x + 15 = 6
  • Combine like terms: 2x + 23 = 6

Step 3: Solve for the Variable

  • Isolate the variable by moving constants to the other side: 2x = 6 – 23
  • Perform the subtraction: 2x = -17
  • Divide both sides by 2 to solve for x: x = -17/2

Step 4: Check Your Solution

Substitute x = -17/2 back into the original equation:

2/3(-17/2 + 1) – 1/4(2(-17/2) – 5) = 1/2

After simplifying both sides, we can see that the equation holds true. Hence, x = -17/2 is the correct solution.

By following these steps and practicing with different equations, you will become more comfortable and confident in solving equations with fractions. Remember, practice makes perfect!

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