SOLVING MULTI-STEP EQUATIONS & INEQUALITIES��(VARIABLES ON BOTH SIDES)�
Math 8
King Midas has returned and has spent money on more bags to hold gold coins in the gifts he gives his children. So far, we have only seen either the Prince or the Princess receive bags while the other sibling was given loose gold coins. What would the situation look like if a mixture of bags and coins were given to each of them? Could you still determine how many coins are in each bag, if the King loves them both equally? Use the pictures of the following situation to determine how many coins are in each bag. What would the equation look like?
Week 1: How many coins are in each bag?
Princess
Prince
Set aside 2 bags from each child.
=
Week 1: How many coins are in each bag?
Princess
Prince
Set aside 2 bags from each child.
=
=
Each bag contains 7 coins
Week 2: How many coins are in each bag?
Princess
Prince
Set aside 4 bags from each child.
=
Week 2: How many coins are in each bag?
Princess
Prince
Set aside 4 bags from each child.
=
The only way for this to be true is
if the bags have zero coins inside
0
Week 3: How many coins are in each bag?
Princess
Prince
Set aside the same amount of bags
and coins from each child.
=
Week 3: How many coins are in each bag?
Princess
Prince
Set aside the same amount of bags
and coins from each child.
=
Each bag contains 2 coins
Split the remaining items into equal groups
Week 4: How many coins are in each bag?
Prince
Princess
Set aside the same amount of bags
and coins from each child.
Week 4: How many coins are in each bag?
Prince
Princess
Set aside the same amount of bags
and coins from each child.
Split the remaining items into equal groups
Each bag contains 2 coins
Week 5: How many coins are in each bag?
Prince
Princess
Open the boxes
Week 5: How many coins are in each bag?
Prince
Princess
Split the remaining items into equal groups
Each bag contains 2 coins
=
Set aside the same amount of bags
and coins from each child.
Week 6: How many coins are in each bag?
Princess
Prince
Open the boxes
Week 6: How many coins are in each bag?
Princess
Prince
Open the boxes
Split the remaining items
into equal groups
Each bag contains 2 coins
Set aside the same amount of bags
and coins from each child.
Steps for Solving Multi-Step Equations:
1. Use the Distributive Property to eliminate parentheses and combine any like terms on the same side of the equation/inequality
-there should be at most two terms on either side
3. Use inverse operations to solve the 2-step equation/inequality that remains
4. Check your solution!!
2. Use addition or subtraction to move all variables to one side of the problem
Solve each equation or inequality
Check your solution!
Replacing the variable with the found solution
resulted in both sides being equal
Solve each equation or inequality
If one side becomes ZERO
while the other has 2 terms
that is not desirable
Solve each equation or inequality
10 11 12 13 14
Solve each equation or inequality
Solve each equation or inequality
Check your solution!
Solve each equation or inequality
−5
−6
Billy and Jane both have lemonade stands where x represents the number of glasses of lemonade they have sold. Billy’s profit can be represented by the expression 0.5x – 4. Jane’s profit can be represented by the expression 0.75x – 10. How many glasses of lemonade would they have to sell in order to have the same profit?
If Billy and Jane sell
24 glasses of lemonade
they will have the same
profit