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Solving Equations
How Many Solutions?
Word Problems
100
1/2x - 2 = 4
1/2x - 2 = 4

         +2    +2

      1/2x = 6

       ×2        ×2

          x  = 12

100

How many solutions?

x = x

Infinite Solutions!

200
-2y + 8 = 18
-2y + 8 = 18

        -8     -8

       -2y = 10

        /-2     /-2

         y  =  -5

200

How many solutions?

3 = 5

No Solutions

300
5x = 2x + 12
5x = 2x + 12
-2x   -2x
3x = 12
/3      /3

x   =  4


300

How many solutions?

4x - 7 = 13

Final equation: x = 5

1 Solution

300

Two players, John and Pele, are saving up V-Bucks to buy the next Battle Pass.

  • John already has 200 V-Bucks in his account. He completes daily quests to earn 50 V-Bucks each day.

  • Pele only has 100 V-Bucks. However, he plays more matches and earns 100 V-Bucks each day.

After how many days will John and Pele have the exact same amount of V-Bucks?

50x + 200 = 100x + 100

x = 2

2 days


400
Circle the mistake:
-3(-x - 2) = 2(x - 12)
 3x - 6  = 2x - 24

        +6         +6

       3x  =  2x - 18

      -2x     -2x

          x = -18

-3(-x - 2) = 2(x - 12)
 3x - 6  = 2x - 24

Should be positive 6

Negative times negative is a positive

400

How many solutions?

2x + 4 = 2x - 4

No Solutions

4 is not equal to -4 after the 2x's cancel out

400

Maya and Leo are saving up for a new game.

  • Maya already has $40 saved. She plans to save $5 each week.

  • Leo only has $10 saved. However, he is determined to catch up and plans to save $15 each week.

After how many weeks will Maya and Leo have the exact same amount of money?

5x + 40 = 15x + 15

x = 3

3 weeks

500

-2(x + 4) + 3x = 4(x - 1) - 13

x = 3 

500

How many solutions?

5x = 2x

Final Equation: x = 0

1 solution

500

Two basketball players are competing to see who will have the most total points by the end of the season.

  • Mia has already scored 100 points this season. She averages 15 points per game.

  • Kai started the season late and only has 40 points. However, he is on a hot streak and averages 25 points per game.

After how many games will Mia and Kai have scored the exact same total number of points?

15x + 100 = 25x + 40

x = 6

6 games