Solving Equations with No Solution and Infinite Solutions

Front

What does it mean when an equation has no solution?

Back

An equation has no solution when there are no values that can satisfy the equation, often resulting in a contradiction.

Front

What does it mean when an equation has infinite solutions?

Back

An equation has infinite solutions when any value of the variable satisfies the equation, typically when both sides of the equation are equivalent.

Front

Solve: 8m + 12 = 2(4m + 6)

Back

Infinite Solutions

Front

Solve: 3x + 15 = 3(x + 5)

Back

Infinitely Many Solutions

Front

Solve: 5x - 14 = 8x + 4

Back

-6

Front

Solve: 6(m + 3) = 2(m + 5)

Back

m = -2

Front

Solve: 14 - 2(3p + 1) = 6(4 + p)

Back

p = -1

Front

What is a contradiction in an equation?

Back

A contradiction occurs when simplifying an equation leads to a false statement, indicating no solutions exist.

Front

What is the identity in an equation?

Back

An identity is an equation that is true for all values of the variable, indicating infinite solutions.

Front

How do you determine if an equation has no solution?

Back

To determine if an equation has no solution, simplify it to see if it leads to a false statement, like 0 = 5.