IXL | Create equations with no solutions or infinitely many solutions

Find the missing number so that the equation has no

solutions.

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ref_doc_title.

Learn with an example

question

Find the missing number so that the equation has no

solutions.

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key idea

An equation has no solutions if no value of the variable makes the equation true.

solution

To find the missing number, compare both sides of the equation. If the variable terms are the same and the constant terms are different, then the equation has no solutions.

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The missing number is part of a variable term, so compare the constant terms first. The constant term on the left side of the equation is

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and the constant term on the right side is 11.

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So, the constant terms are different.

This means the equation has no solutions if the variable terms are the same. Look at the variable terms.

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The variable term on the right side is

so the variable term on the left side should also be

The variable terms are the same if the missing number is 2.

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So, the equation has no solutions if the missing number is 2.

You can check that the equation has no solutions when the missing number is 2. Try solving for

Subtract

from both sides.

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No value of

makes this true. It is never true that

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equals 11.

So, the equation has no solutions if the missing number is 2.

Looking for more? Try these:

Lesson: Equations with infinitely many or no solutions

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Teacher tools

Work it out

Not feeling ready yet? These can help:

M.20Find the number of solutions

Lesson: Equations with infinitely many or no solutions

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