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Math Review: Solving Equations

Can you put the following steps in order?


 Check by substituting the variable with the solution / answer


 Divide or Multiply on both sides of the equal sign (Division or Multiplication Property)


 Combine Like Terms on both sides of the equal sign


 Distribute Coefficient(s) (Distributive Property)


 Add a positive or a negative on both sides of the equal sign(Addition Property)

* * * *





Steps in the Correct Order:


1. Distribute Coefficient(s)


2. Combine Like Terms on both sides of the equal sign


3. Add a positive or a negative on both sides of the equal sign


4. Divide or /multiply on both sides of the equal sign


5. Check by substituting the variable with the solution / answer




Do you know the purpose of each step?


1. Distribute Coefficient(s) (Distributive Property)

To eliminate parentheses


2. Combine Like Terms on both sides of the equal sign

To total like terms on both sides of the equal sign


3. Add a positive or a negative on both sides of the equal sign

To isolate the variable or variable term (for example X or 5X)


4. Divide or /multiply on both sides of the equal sign

To isolate the coefficient from the variable term if necessary


5. Check by substituting the variable with the solution / answer

To verify the solution balances the equation; if so, the check confirms the solution is correct.





Here are two mnemonics to remember the order of the steps to solve an equation?


Daily Calculating A's Doing Math Carefully

or

Daisy Chews Almonds Mooing Continuously


Let's Practice!

5m + 2(2m + 3) = -20 - m – 4


• Distribute

• Results = => 5m + 4m + 6 = -20 –m - 4


Combine

• Results = => 9m + 6 = -24 - m


Add (+m) on both sides

• Results = => 10m + 6 = -24


Add (-6) on both sides

• Results = => 10m = -30


Divide by 10 on both sides

• Solution => m= -3




Check:

5m + 2(2m + 3) = -20 - m – 4

5(-3) + 2(2(-3) + 3 ) = -20 – (-3) – 4

5(-3) + 2(-6 + 3) = (-21)

5(-3) + 2(-3) = (- 21)

(-21) = (-21)

Since both sides of the equation have the same number, the equation is balanced. Therefore the solution m = (-3) is correct.

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