Equations with Fractions on Both Sides
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The document provides steps for solving equations with fractions that involve the same variable on both sides. It explains that these types of equations cannot be solved using traditional back-tracking methods. The extra steps include: 1) cross multiplying using brackets to remove fractions, 2) identifying the smaller letter term on both sides, and 3) applying the opposite operation to this term on both sides before simplifying and solving as normal. It then works through examples demonstrating these steps, such as solving the equation n-3=n+6/2/3.
Equations with Fractions on Both Sides
- 2. Solve the Equation : n-3 = n+6 2 3 We cannot solve this Equation using “Onion Skins” or “Back-Tracking”, because our Equation has Fractions and the Variable letter “n” is on both sides of the Equation. WE NEED TO DO SOME EXTRA STEPS BEFORE WE CAN SOLVE THE EQUATION
- 3. Solve the Equation : n-3 = n+6 2 3 The Extra Steps are: 1. Cross Multiply using Brackets (to remove fractions) 2. Identify the smaller letter term (letters both sides step) 3. Apply the Opposite Operation ( + or - ) to this smaller item on both sides. 4. Simplify and Solve the Equation as normal.
- 4. Solve the Equation : 1a. Cross Multiply : 1b. Use Brackets : 1c. Expand Out : n-3 = n+6 2 3 n-3 = n+6 2 3 3 (n - 3) = 2 (n + 6) 3n - 9 = 2n + 12 Now solve as letter both sides (see next slide)
- 5. Finish off our previous question as a variable both sides type question (Eg.Apply Opposites) 3n - 9 - 2n n–9 +9 n = 2n + 12 - 2n = 12 +9 = 21
- 6. Solve the Equation : 8h + 7 = 3h - 4 2 1a. Cross Multiply : 8h + 7 = 3h -4 2 1b. Use Brackets : 1 (8h + 7) 1c. Expand Out : 8h + 7 1 = 2 (3h - 4) = 6h - 8 Now solve as letter both sides (see next slide)
- 7. Finish off our previous question as a variable both sides type question (Eg.Apply Opposites) 8h + 7 - 6h 2h + 7 -7 2h /2 h = 6h - 8 - 6h = -8 -7 = -15 /2 = -7.5 or -7 ½
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