What does it mean if an equation has one solution?

It means there is exactly one value of the variable that makes the equation true.

What does it mean if an equation has no solution?

It means there is no value of the variable that can satisfy the equation.

What does it mean if an equation has infinite solutions?

It means any value of the variable will satisfy the equation.

Give an example of an equation with infinite solutions.

Example: $$3(x + 1) = 3x + 3$$ .

What is the significance of the number of solutions in equations?

It helps determine the relationship between variables and the nature of the equation.

Resource Library

Math

Algebra

Equations With No Solutions

Equations: One Solution, No Solution, Infinite Solutions

Equations: One solution, No solution, Infinite solutions

Flashcard

•

Mathematics

•

8th Grade

•

Practice Problem

•

Hard

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FLASHCARD QUESTION

Front

What is an equation with one solution?

Back

An equation that can be solved to find a single value for the variable. Example: $x = 5$ .

FLASHCARD QUESTION

Front

What is an equation with no solution?

Back

An equation that has no values for the variable that can satisfy it. Example: $x + 2 = x - 3$ .

FLASHCARD QUESTION

Front

What is an equation with infinite solutions?

Back

An equation that is true for all values of the variable. Example: $2x + 4 = 2(x + 2)$ .

FLASHCARD QUESTION

Front

How many solutions does $16 = y$ represent?

Back

One solution.

FLASHCARD QUESTION

Front

How many solutions does $-y = -y$ represent?

Back

Infinite solutions.

FLASHCARD QUESTION

Front

How many solutions does $14 = 14$ represent?

Back

Infinite solutions.

FLASHCARD QUESTION

Front

How many solutions does $9x - 2 = -2 + 9x$ represent?

Back

Infinite solutions.

FLASHCARD QUESTION

Front

How many solutions does $x = -6$ represent?

Back

One solution.

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