Solving Equations with Fractions on Both Sides

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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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