# 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?**

**D**aily** C**alculating** A**'s **D**oing **M**ath **C**arefully

or

**D**aisy **C**hews **A**lmonds **M**ooing **C**ontinuously

**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.