Equations with Variables on Both Sides

All

100

2x + 5 = 13

x = 4

200

2x + 3x = 15 

x = 3

300

-3(x+2) = 6

x = -4

400

28 - 4x = x - 17

x = 9

500

In the equation 2(x + 4) = 2x + 8, which number(s) should be changed to make the equation have no solutions?

You can change the 4 or the 8 so the sides will have different constants. 

Of

100

3x - 12 = 6

x = 6

200

4x - x = -9

x = -3

300

−3(4x−8)=−36

x = 5

400

39 - 3x = x + 7

x = 8

500

If the equation 5(3x+6)=3(5x+k) has infinitely many solutions, what is the value of k?

k = 10 so each side will have the variable of 30. 

These

100

-2x - 1 = 7

x = -4

200

7x + 8x + 5x = 20

x = 1

300

6(−x−3) = 24

x = -7

400

13x + 8 = 10 + 12x

x = 2

500

x−1=5x+3x−8

x = 1

Are

100

-10 = 4 - 2x

x = 7 

200

-3x - 2x - 7x = 24

x = -2

300

3(−6x−5) = 75

x = -5

400

x - 4 = 28 + 5x

x = -8

500

−18−6x=6(1+3x)

x = -1

Random

100

2x + 1 = 1

x = 0

200

16 = x + 7x 

x = 2

300

5(1 - 2x)= 85

x = -8

400

20x - 11 = 4 + 15x

x = 3

500

Give an example of an equation with variables on both sides with exactly one solution and explain why it has one solution.

Any equation with different coefficients is correct.