Mastering Algebra Equations with Fractions: Step-by-Step Solutions

Solving algebra equations with fractions involves a series of steps to isolate the variable (usually represented as 'x') on one side of the equation. Here's a step-by-step guide on how to solve such equations:

Step 1: Clear the Equation of Fractions (if necessary):

• If the equation has fractions, it's often easier to start by clearing the fractions. You can do this by multiplying both sides of the equation by the least common multiple (LCM) of the denominators.

Step 2: Simplify Both Sides:

• After clearing fractions, simplify both sides of the equation by performing any necessary operations (addition, subtraction, multiplication, division) to simplify it as much as possible.

Step 3: Isolate the Variable:

• Add or subtract terms on both sides of the equation to get all terms containing 'x' on one side and constants on the other side.

Step 4: Solve for 'x':

• Once the variable is isolated on one side of the equation, solve for 'x' by performing the required operations to isolate 'x' on one side. This may involve additional simplification steps.

Step 5: Check Your Solution:

• Always check your solution by plugging the value of 'x' back into the original equation to ensure it satisfies the equation. If it does, then you have found the correct solution.

Here's an example to illustrate these steps:

Example:Solve for 'x' in the equation: (3/4)x + 2 = 5

Step 1: Clear Fractions (not needed in this case):

• The equation doesn't have fractions to clear, so we can proceed to simplify.

Step 2: Simplify:

• (3/4)x + 2 = 5

Step 3: Isolate the Variable:

• Subtract 2 from both sides of the equation:(3/4)x = 5 - 2(3/4)x = 3

Step 4: Solve for 'x':

• To isolate 'x', multiply both sides by the reciprocal of (3/4), which is (4/3):x = (3 * 4) / 3x = 12 / 3x = 4

Step 5: Check the Solution:

• Plug 'x' back into the original equation:(3/4)(4) + 2 = 53 + 2 = 5

Since the equation is true when 'x' is 4, this is the correct solution.

Keep in mind that when working with equations containing fractions, it's important to be patient and meticulous in your calculations. Carefully perform each step to ensure accuracy and arrive at the correct solution.