Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

Equations with Variables on Both Sides

18,530 views

Published on

Solving Equations with Letter Variables on Both Sides

Published in: Education, Technology
  • Be the first to comment

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

×