7.4 Equations with No Solutions or Infinitely Many Solutions

MATHEMATICS OBJECTIVE

Students will be able to:

Determine the number of solutions to an equation.

ESSENTIAL UNDERSTANDING

Equations with one variable can have zero, one, or infinitely many solutions. An equation with one solution is only true for a single value of the variable. An equation with infinitely many solutions is true for any value of the variable. An equation with no solutions is not true for any value of the variable.

7.3 Blank Notes

7.3

7.3 Dice Activity Data Sheet

I can determine the number of solutions to an equation.

TYPES OF SOLUTIONS

INFINITELY MANY SOLUTIONS

A one-variable equation has infinitely many solutions when solving results

in a true statement, such as 2 = 2.

ONE SOLUTION

A one-variable equation has one solution when solving results in one value

for the variable, such as x = 2.

NO SOLUTION

A one-variable equation has no solution when solving results in an untrue

statement, such as 2 = 3.

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