2.4 One Solution, No Solution, Infinitely Many Solutions

Front

What does it mean if an equation has one solution?

Back

An equation has one solution when there is exactly one value of the variable that makes the equation true.

Tags

CCSS.8.EE.C.7A

Front

What does it mean if an equation has no solution?

Back

An equation has no solution when there is no value of the variable that can satisfy the equation.

Tags

CCSS.8.EE.C.7A

Front

What does it mean if an equation has infinitely many solutions?

Back

An equation has infinitely many solutions when any value of the variable makes the equation true.

Tags

CCSS.8.EE.C.7A

Front

Solve: 3x − 3 = −3 + 3x

Back

Infinitely Many Solutions

Tags

CCSS.8.EE.C.7A

Front

Solve: −5 + 7x = 7x + 5

Back

No Solutions

Tags

CCSS.8.EE.C.7A

Front

Solve: 5.5 - x = -4.5 - x

Back

No Solution

Tags

CCSS.8.EE.C.7A

Front

Solve: 3(−2x − 6) = −6x − 8

Back

No Solutions

Tags

CCSS.8.EE.C.7B

Front

What is the first step to determine the number of solutions of an equation?

Back

Simplify both sides of the equation if possible.

Tags

CCSS.8.EE.C.7B

Front

What is a key indicator of infinitely many solutions in an equation?

Back

If both sides of the equation simplify to the same expression.

Tags

CCSS.8.EE.C.7A

Front

What is a key indicator of no solutions in an equation?

Back

If simplifying leads to a false statement, such as 0 = 5.

Tags

CCSS.8.EE.C.7A