IXL | Find the number of solutions

How many solutions does this equation have?

2t = 1 + 2t

no solution

one solution

infinitely many solutions

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Learn with an example

question

How many solutions does this equation have?

0 = ^–9m + 9m

no solution

one solution

infinitely many solutions

key idea

If solving an equation yields a statement that is false, like 4 = 3, then the equation has no solution.

If solving an equation yields a statement that is true for a single value for the variable, like x = 3, then the equation has one solution.

If solving an equation yields a statement that is always true, like 3 = 3, then the equation has infinitely many solutions.

solution

Solve for m.

^–9m + 9m

Combine like terms

The statement 0 = 0 is true for every value of m. So, the equation is an identity and has infinitely many solutions.

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.15Solve equations using the distributive property

M.1Which x satisfies an equation?

Lesson: Equations with infinitely many or no solutions

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