Solving Equations with Letter Variables on Both Sides

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2. Solve the Equation :
3n + 5 = 2n + 7
We cannot solve this Equation using “Onion
Skins” or “Back-Tracking”, because our
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 :
3n + 5 = 2n + 7
The Extra Steps are:
1. Identify the smaller letter term.
2. Apply the Opposite Operation ( + or - ) to
this smaller item on both sides.
3. Simplify and Solve the Equation as normal.

4. 3n + 5 = 2n + 7
Step 1. Identify the smaller letter term.
3n + 5 = 2n + 7
Step 2. SUBTRACT it from both sides
3n + 5 = 2n + 7
-2n
-2n
n+5=
7
Step 3. Solve as normal (See next slide)

5. Step 3. Solve the Equation :
n+5=7
n+5=7
To solve the Equation work from the biggest outer
skin, inwards through the smaller skins, applying
opposites, until we reach the letter variable.
Solution for n is 7 - 5 = 2

6. 11 – 5h = 3h + 3
-
Step 1. Identify the smaller letter term.
11 – 5h = 3h + 3
-
Step 2. ADD it to both sides
11 – 5h = 3h + 3
+5h +5h
11
= 2h + 3
-
Step 3. Solve as normal (See next slide)

7. 11 = 2h + 3 is the same as 2h + 3 = 11
2h + 3 = 11
To solve the Equation work from the biggest outer
skin, inwards through the smaller skins, applying
opposites, until we reach the letter variable.
Solution for h is 11 - 3
2 =4

8. Solve :
5(n + 1) = 2(n + 20)
We cannot solve this Equation using “Onion
Skins” or “Back-Tracking”, because our
Brackets and the Variable letter “n”
are on both sides of the Equation.
WE NEED TO EXPAND THE BRACKETS
BEFORE WE CAN SOLVE THE EQUATION

9. 5(n + 1) = 2(n + 10)
5(n + 1) = 2(n + 10)
5n + 5 = 2n + 20
Now Solve a Letters Both Sides Equation
5n + 5 = 2n + 20
-2n
-2n
3n + 5 =
20
Step 3. Solve as normal (See next slide)

10. We can solve 3n + 5 = 20 with Onion Skins
3n + 5 = 20
To solve the Equation work from the biggest outer
skin, inwards through the smaller skins, applying
opposites, until we reach the letter variable.
Solution for h is 20 - 5
3 =5

11. Working Out Steps are:
1. Expand any Brackets First
2. Identify the smaller letter term.
3. Apply the Opposite Operation ( + or - ) to
this smaller item on both sides.
4. Simplify and Solve the Equation as normal*.
(* Use Onion Skins, Algebra Reversing,
or Backtracking with Flowcharts )

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