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# Equations with Variables on Both Sides

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Solving Equations with Letter Variables on Both Sides

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### Equations with Variables on Both Sides

1. 1. Image Source: http://oliveloafdesign.wordpress.com
2. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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 )
12. 12. http://passyworldofmathematics.com/ All Images and Diagrams are Copyright by Passy’s World of Mathematics