Common Core: High School - Algebra : Solve Simple Rational and Radical One Variable Equations, Show Extraneous Solutions: CCSS.Math.Content.HSA-REI.A.2

Example Questions

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Example Question #1 : Solve Simple Rational And Radical One Variable Equations, Show Extraneous Solutions: Ccss.Math.Content.Hsa Rei.A.2

Solve for .

Explanation:

To solve for , square both terms to cancel out the square root sign on the left-hand side.

Next, add two to both sides of the equation.

_____________

From here, check for extraneous solutions by substituting the value found for  into the original equation.

Since the square root of one is either positive or negative one, the solution found is verified.

Example Question #2 : Solve Simple Rational And Radical One Variable Equations, Show Extraneous Solutions: Ccss.Math.Content.Hsa Rei.A.2

Solve for .

Explanation:

To solve for , first subtract one from both sides.

____________________

From here, divide both sides by negative one.

Next, square both sides to cancel the square root sign on the left-hand side.

Now, subtract one from both sides to solve for .

____________

Lastly, check for extraneous solutions by substituting the value found for  into the original equation.

Example Question #3 : Solve Simple Rational And Radical One Variable Equations, Show Extraneous Solutions: Ccss.Math.Content.Hsa Rei.A.2

Solve for .

Explanation:

To solve for , add two to both sides of the equation.

______________

Now, multiply by  on both sides. This will move the variable from the denominator on one side to the numerator of the other side.

Lastly, divide both sides by twelve.

The twelve in the numerator and the twelve in the denominator cancel out thus, solving for .

Example Question #4 : Solve Simple Rational And Radical One Variable Equations, Show Extraneous Solutions: Ccss.Math.Content.Hsa Rei.A.2

Solve for .

Explanation:

To solve for , first subtract four from both sides so all constants are on one side.

_____________

Now, square both sides to cancel the square root sign on the left-hand side.

Recall that when a negative number is squared the result is always a positive value.

From here, check for extraneous solutions by substituting in the value found for .

Since the square root of a value results in a positive and a negative value, our solution is verified.

Example Question #5 : Solve Simple Rational And Radical One Variable Equations, Show Extraneous Solutions: Ccss.Math.Content.Hsa Rei.A.2

Solve for .

Explanation:

To solve for  start by squaring both sides to eliminate the square root sign.

From here multiply both sides by two. On the left-hand side, the two in the numerator will cancel out the two in the denominator.

From here, check for extraneous solutions by substituting in the value found for  into the original equation.

Thus, the solution is verified.

Example Question #6 : Solve Simple Rational And Radical One Variable Equations, Show Extraneous Solutions: Ccss.Math.Content.Hsa Rei.A.2

Solve for .

Explanation:

To solve for , first add two to both sides.

____________

From here, multiply both sides by

Now divide by seven to solve for .

The seven in the numerator and seven in the denominator cancel out, thus solving for .

Example Question #7 : Solve Simple Rational And Radical One Variable Equations, Show Extraneous Solutions: Ccss.Math.Content.Hsa Rei.A.2

Solve for .

Explanation:

To solve for , first square both sides of the equation. Squaring a square root sign will cancel them out.

Now, subtract five from both sides to get all constants on one side of the equation while all variables are on the other side of the equation.

_____________

From here, divide by negative one on both sides.

Lastly, check for extraneous solutions by substituting in the value found for  into the original equation.

Thus, the solution is verified.

Example Question #8 : Solve Simple Rational And Radical One Variable Equations, Show Extraneous Solutions: Ccss.Math.Content.Hsa Rei.A.2

Solve for .

Explanation:

To solve for , simply multiply both sides of the equation by two.

The two in the numerator cancels the two in the denominator, thus solving for .

Example Question #9 : Solve Simple Rational And Radical One Variable Equations, Show Extraneous Solutions: Ccss.Math.Content.Hsa Rei.A.2

Solve for .

Explanation:

To solve for , first divide by two.

The two in the denominator cancels the two in the numerator.

From here, square both sides of the equation. Squaring a square root cancels it out.

To check for extraneous solutions, simply substitute into the original equation the value found for .

Example Question #10 : Solve Simple Rational And Radical One Variable Equations, Show Extraneous Solutions: Ccss.Math.Content.Hsa Rei.A.2

Solve for .

Explanation:

To solve for , add three to both sides of the equation.

______________

From here, take the square root of both sides. Taking the square root of a squared term eliminates the square.

Next, check for extraneous solutions. Substitute each potential solution into the original equation to verify if it results in a legal solution.

Substituting in positive four.

Substituting in negative four.

Therefore, both answers are verified solutions.

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