Multistep Equations- How many Solutions?

Two-Step Equations

100

2x+4=12

 x=4

200

5x-3=27

x = 6

300

x/2 + 4=7

x = 6

400

12=2x+10

x = 1

500

2-3x=-28

x = 10

Multi-step Equations

100

3(x+3)=15

x = 2

200

3x+4x+5=2x+10

 x=2

300

3(x+2)+2=4x+2

 x=6

400

x + x+ 3x+5=12

 x=1

500

15x-15x+3x=2x+10

x = 10

Infinitely Many, No Solution, One Solution

100

2x+6=2x+6

infinitely many solutions

200

2x-6=2x+6

 No solution

300

3(x-4)=3x+4

No solution

400

3x+2x+4=4x-1

 x=-5

 One solution

500

5x+y=5x+y

Infinitely Many Solutions

Math Skills

100

Explain how you know an equation has infinitely many solutions

Both sides of the equation are the same

200

What makes an equation have no solution?

An equation has NO solution when the variables cancel out and leave a false statement. For example, 3=7

300

Explain how you know an equation has one solution?

The variable terms on both sides must have different coefficients

400

Fill in the blank so that the equation will have NO solution: 

          4x - 5 = __ + 7

  4x - 5 = 4x + 7

500

Fill in the blank so that the equation will have ONE solution: 

          4x - 5 = __ + 7

Any x term other than 4x