Common Core: 8th Grade Math : Expressions & Equations

Study concepts, example questions & explanations for Common Core: 8th Grade Math

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Example Questions

Example Question #1 : How To Find Out When An Equation Has No Solution

Solve the equation:  

Possible Answers:

No solution

Correct answer:

No solution

Explanation:

Notice that the end value is a negative.  Any negative or positive value that is inside an absolute value sign must result to a positive value.

If we split the equation to its positive and negative solutions, we have:

Solve the first equation.

The answer to  is: 

Solve the second equation.

The answer to  is:   

If we substitute these two solutions back to the original equation, the results are positive answers and can never be equal to negative one.

The answer is no solution. 

Example Question #1 : Give Examples Of Linear Equations: Ccss.Math.Content.8.Ee.C.7a

Select the option that describes the solution(s) for the following equation:

Possible Answers:

Infinitely many solutions 

No solution

One solution 

Correct answer:

No solution

Explanation:

Let's begin by discussing our answer choices:

In order for an equation to have no solution, the equation, when solved, must equal a false statement; for example,

In order for an equation to have one solution, the equation, when solved for a variable, but equal a single value; for example,

In order for an equation to have infinitely many solutions, the equation, when solved, must equal a statement that is always true; for example,  

To answer this question, we can solve the equation:

This equation equals a false statement; thus, the correct answer is no solution.  

Example Question #2 : Give Examples Of Linear Equations: Ccss.Math.Content.8.Ee.C.7a

Select the option that describes the solution(s) for the following equation:

 

Possible Answers:

Infinitely many solutions 

No solution

One solution 

Correct answer:

No solution

Explanation:

Let's begin by discussing our answer choices:

In order for an equation to have no solution, the equation, when solved, must equal a false statement; for example, 

In order for an equation to have one solution, the equation, when solved for a variable, but equal a single value; for example, 

In order for an equation to have infinitely many solutions, the equation, when solved, must equal a statement that is always true; for example,  

To answer this question, we can solve the equation:

This equation equals a false statement; thus, the correct answer is no solution.  

Example Question #3 : Give Examples Of Linear Equations: Ccss.Math.Content.8.Ee.C.7a

Select the option that describes the solution(s) for the following equation:

 

Possible Answers:

Infinitely many solutions 

One solution 

No solution

Correct answer:

No solution

Explanation:

Let's begin by discussing our answer choices:

In order for an equation to have no solution, the equation, when solved, must equal a false statement; for example, 

In order for an equation to have one solution, the equation, when solved for a variable, but equal a single value; for example, 

In order for an equation to have infinitely many solutions, the equation, when solved, must equal a statement that is always true; for example,  

To answer this question, we can solve the equation:

This equation equals a false statement; thus, the correct answer is no solution.  

 

Example Question #4 : Give Examples Of Linear Equations: Ccss.Math.Content.8.Ee.C.7a

Select the option that describes the solution(s) for the following equation:

 

Possible Answers:

Infinitely many solutions 

One solution 

No solution

Correct answer:

No solution

Explanation:

Let's begin by discussing our answer choices:

In order for an equation to have no solution, the equation, when solved, must equal a false statement; for example, 

In order for an equation to have one solution, the equation, when solved for a variable, but equal a single value; for example, 

In order for an equation to have infinitely many solutions, the equation, when solved, must equal a statement that is always true; for example,  

To answer this question, we can solve the equation:

This equation equals a false statement; thus, the correct answer is no solution.  

Example Question #3 : Give Examples Of Linear Equations: Ccss.Math.Content.8.Ee.C.7a

Select the option that describes the solution(s) for the following equation:

 

Possible Answers:

Infinitely many solutions 

No solution

One solution 

Correct answer:

Infinitely many solutions 

Explanation:

Let's begin by discussing our answer choices:

In order for an equation to have no solution, the equation, when solved, must equal a false statement; for example, 

In order for an equation to have one solution, the equation, when solved for a variable, but equal a single value; for example, 

In order for an equation to have infinitely many solutions, the equation, when solved, must equal a statement that is always true; for example,  

To answer this question, we can solve the equation:

This equation equals a statement that is always true; thus, the correct answer is infinitely many solutions.  

Example Question #161 : Grade 8

Select the option that describes the solution(s) for the following equation:

 

Possible Answers:

Infinitely many solutions 

No solution

One solution 

Correct answer:

Infinitely many solutions 

Explanation:

Let's begin by discussing our answer choices:

In order for an equation to have no solution, the equation, when solved, must equal a false statement; for example, 

In order for an equation to have one solution, the equation, when solved for a variable, but equal a single value; for example, 

In order for an equation to have infinitely many solutions, the equation, when solved, must equal a statement that is always true; for example,  

To answer this question, we can solve the equation:

This equation equals a statement that is always true; thus, the correct answer is infinitely many solutions.  

Example Question #162 : Grade 8

Select the option that describes the solution(s) for the following equation:

 

Possible Answers:

One solution

No solution

Infinitely many solutions 

Correct answer:

Infinitely many solutions 

Explanation:

Let's begin by discussing our answer choices:

In order for an equation to have no solution, the equation, when solved, must equal a false statement; for example, 

In order for an equation to have one solution, the equation, when solved for a variable, but equal a single value; for example, 

In order for an equation to have infinitely many solutions, the equation, when solved, must equal a statement that is always true; for example,  

To answer this question, we can solve the equation:

This equation equals a statement that is always true; thus, the correct answer is infinitely many solutions.  

Example Question #163 : Grade 8

Select the option that describes the solution(s) for the following equation:

 

Possible Answers:

One solution 

No solution

Infinitely many solutions 

Correct answer:

One solution 

Explanation:

Let's begin by discussing our answer choices:

In order for an equation to have no solution, the equation, when solved, must equal a false statement; for example, 

In order for an equation to have one solution, the equation, when solved for a variable, but equal a single value; for example, 

In order for an equation to have infinitely many solutions, the equation, when solved, must equal a statement that is always true; for example,  

To answer this question, we can solve the equation:

This equation equals a single value; thus, the correct answer is one solution.  

Example Question #164 : Grade 8

Select the option that describes the solution(s) for the following equation:

 

Possible Answers:

One solution

Infinitely many solutions 

No solution

Correct answer:

One solution

Explanation:

Let's begin by discussing our answer choices:

In order for an equation to have no solution, the equation, when solved, must equal a false statement; for example, 

In order for an equation to have one solution, the equation, when solved for a variable, but equal a single value; for example, 

In order for an equation to have infinitely many solutions, the equation, when solved, must equal a statement that is always true; for example,  

To answer this question, we can solve the equation:

This equation equals a single value; thus, the correct answer is one solution.  

 

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