 # Solutions of Equations

Related Topics:
Common Core for Mathematics
More Math Lessons for Grade 8

Examples, solutions, videos and lessons to help Grade 8 students learn how to solve linear equations in one variable.

A. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = aa = a, or a = b results (where a and b are different numbers).

B. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Common Core: 8.EE.7a

### Suggested Learning Targets

• I can give examples of linear equations in one variable with one solution and show that the given example equation has one solution by successively transforming the equation into an equivalent equation of the form x=a
• I can give examples of linear equations in one variable with infinitely many solutions and show that the given example has infinitely many solutions by successively transforming the equation into an equivalent equation of the form a=a
• I can give examples of linear equations in one variable with no solution and show that the given example has no solution by successively transforming the equation into an equivalent equation of the form b=a, where a and b are different numbers.

The following table shows examples of linear equations in one variable with one, none, or many solutions. Scroll down the page for more examples and solutions. Finding examples of linear equations in one variable with one, none, or many solutions (8.EE.7a)

Solving One-Variable Linear Equations (8.EE.7)

One Solution, No Solution, Infinite Solutions to Equations
How to determine if an equation has one solution (which is when one variable equals one number), or if it has no solution (the two sides of the equation are not equal to each other) or infinite solutions (the two sides of the equation are identical)? Solving Equations with different types of solutions. Number of solutions to linear equations.

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 