### All Common Core: 8th Grade Math Resources

## Example Questions

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

Solve the rational equation:

**Possible Answers:**

no solution

or

**Correct answer:**

no solution

With rational equations we must first note the domain, which is all real numbers except** **and** **. That is, these are the values of that will cause the equation to be undefined. Since the least common denominator of , , and is , we can mulitply each term by the LCD to cancel out the denominators and reduce the equation to . Combining like terms, we end up with . Dividing both sides of the equation by the constant, we obtain an answer of . However, this solution is NOT in the domain. Thus, there is NO SOLUTION because is an extraneous answer.

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

How many solutions does the equation below have?

**Possible Answers:**

No solutions

Two

One

Three

Infinite

**Correct answer:**

No solutions

When finding how many solutions an equation has you need to look at the constants and coefficients.

The coefficients are the numbers alongside the variables.

The constants are the numbers alone with no variables.

If the coefficients are the same on both sides then the sides will not equal, therefore no solutions will occur.

Use distributive property on the right side first.

No solutions

### Example Question #4 : How To Find Out When An Equation Has No Solution

Solve:

**Possible Answers:**

**Correct answer:**

First factorize the numerator.

Rewrite the equation.

The terms can be eliminated.

Subtract one on both sides.

However, let's substitute this answer back to the original equation to check whether if we will get as an answer.

Simplify the left side.

The left side does not satisfy the equation because the fraction cannot be divided by zero.

Therefore, is not valid.

The answer is:

### Example Question #5 : How To Find Out When An Equation Has No Solution

Solve for :

**Possible Answers:**

No solution

**Correct answer:**

No solution

Combine like terms on each side of the equation:

Next, subtract from both sides.

Then subtract from both sides.

This is nonsensical; therefore, there is no solution to the equation.

### Example Question #6 : How To Find Out When An Equation Has No Solution

Solve the equation:

**Possible Answers:**

No solution

**Correct answer:**

No solution

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:**

No solution

Infinitely many solutions

One solution

**Correct answer:**

No solution

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:**

One solution

Infinitely many solutions

No solution

**Correct answer:**

No solution

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

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

Let's begin by discussing our answer choices:

**no solution**, the equation, when solved, must equal a false statement; for example,

**one solution**, the equation, when solved for a variable, but equal a single value; for example,

**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 #5 : 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:**

Infinitely many solutions

Let's begin by discussing our answer choices:

**no solution**, the equation, when solved, must equal a false statement; for example,

**one solution**, the equation, when solved for a variable, but equal a single value; for example,

**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.