Algebra 1 : Linear / Rational / Variable Equations

Study concepts, example questions & explanations for Algebra 1

varsity tutors app store varsity tutors android store

Example Questions

Example Question #3 : How To Find Out When An Equation Has No Solution

Solve:  

Possible Answers:

Correct answer:

Explanation:

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

Solve for :

Possible Answers:

No solution

Correct answer:

No solution

Explanation:

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 #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. 

Learning Tools by Varsity Tutors