Solving Equations with Variables on Both Sides and Special Cases

Solve:

5x + 4 = 5x − 3

• x = 4

• x = -3

• infinitely many solutions

• no solutions

Solve:

2y − 3 = 2y − 3

• y = 0

• y = -3

• infinitely many solutions

• no solutions

Solve:

4x + 1 = 8x − 3

• x = 1

• x = 2

• infinitely many solutions

• no solutions

Solve:

9y − 5 = 2y + 9

• y = -2

• y = 2

• infinitely many solutions

• no solutions

Solve:

3(x − 2) = 3x − 6

• x = 6

• x = -6

• infinitely many solutions

• no solutions

Solve:

6(y + 4) = 6y + 10

• y = 10

• y = 24

• infinitely many solutions

• no solutions

Solve:

10x + 3 + 3x = 5x + 1 + 8x + 2

• x = -3

• x = 3

• infinitely many solutions

• no solutions

Solve:

3x + 1 + 2x = 4x − 2 − 7x + 7

• x = 2

• x = ½

• infinitely many solutions

• no solutions

Solve:

9x + 7 − 5x = 4x − 7

• x = 7

• x = -7

• infinitely many solutions

• no solutions

What does it mean when an equation has one solution?

• the equation is always TRUE when any value is substituted in for the variable

• the equation will NEVER be true when any value is substituted in for the variable

• only ONE solution will make the equation true