How to Solve Linear Equations with Fractions
1. Clear the Fractions
- Multiply every term in the equation by the least common multiple (LCM) of all the denominators to eliminate fractions.
- This will leave you with an equation in whole numbers.
2. Simplify the Equation
- Combine like terms on both sides of the equation.
- Follow the order of operations (PEMDAS) to simplify expressions.
3. Isolate the Variable
- Use inverse operations to isolate the variable on one side of the equation.
- Perform the same operation on both sides to maintain equality.
4. Check Your Solution
- Substitute the solution back into the original equation to ensure it satisfies the equation.
- If the solution doesn't work, recheck your steps for errors.
5. Example:
- Given equation: \( \frac{2}{3}x + \frac{1}{4} = 5 \)
- LCM of 3 and 4 is 12, so multiply each term by 12 to clear fractions:
\( 12 \times \frac{2}{3}x + 12 \times \frac{1}{4} = 12 \times 5 \)
\( 8x + 3 = 60 \)
- Simplify: \( 8x = 57 \)
- Isolate x: \( x = \frac{57}{8} \)
- Check: \( \frac{2}{3}(\frac{57}{8}) + \frac{1}{4} = 5 \) (if it satisfies the equation)
By following these steps, you can effectively solve linear equations with fractions and find the value of the variable.