Warmup

22

1) 4 2 6

2) + 4 = 95

3) 3x + 7 = 58

4) + 3 , if x = 42

x

x

xx

1) Solve. 3x + 2 = 4x - 1

You need to get the variables on one side of the equation. It does not matter which variable you move. Try to move the one that will keep your variable positive.

Let’s see a few examples:

1) 6x - 3 = 2x + 13 -2x -2x 4x - 3 = 13

+3 +3 4x = 16 4 4 x = 4

Be sure to check your answer!

6(4) - 3 =? 2(4) + 13

24 - 3 =? 8 + 13

21 = 21

Let’s try another!

2) 3n + 1 = 7n - 5 -3n -3n 1 = 4n - 5 +5 +5 6 = 4n 4 4Reduce! 3 = n 2

Check:

3(1.5) + 1 =? 7(1.5) - 5

4.5 + 1 =? 10.5 - 5

5.5 = 5.5

Two special cases:

24 + 6y - 3 = 4y - 12 + 2y

21 + 6y = 6y - 12 - 6y - 6y 21 = -12 Never true!21 ≠ -12 NO SOLUTION!

3a + 3 - 5 = 3a - 2

3a - 2 = 3a - 2-3a -3a -2 = -2 Always true!Many solutions or

infinite solutions

Try a few on your own:

• 9x + 7 = 3x - 5

• 8 - 2(y + 1) = -3y + 1

• 8 - 1 z = 1 z - 7 2 4