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

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All Common Core: High School - Algebra Resources

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Example Question #21 : Reasoning With Equations & Inequalities

Solve for .

$\sqrt{2-x}=7+3$

Possible Answers:

x=102

x=-100

x=-98

x=-102

x=98

Correct answer:

x=-98

Explanation:

To solve for , combine the like terms on the right-hand side.

$\sqrt{2-x}=7+3$

$\sqrt{2-x}=10$

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

$(\sqrt{2-x})^2=(10)^2$

2-x=100

Now, subtract two from both sides so that all constants are on one side and all variables are on the other side.

2-x=100

_________________

-x=98

Next, divide both sides by negative one.

$\frac{-x}{-1}=\frac{98}{-1}$

x=-98

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

$\sqrt{2-x}=7+3$

$\\\sqrt{2--98}=7+3 \\\sqrt{100}=10 \\\pm10=10$

Therefore, the solution is verified.

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Example Question #22 : Reasoning With Equations & Inequalities

Solve for .

$2-\sqrt{x+1}=5+3$

Possible Answers:

x=36

x=35

x=-37

x=37

x=-35

Correct answer:

x=35

Explanation:

To solve for , first combine the like terms on the right-hand side of the equation.

$2-\sqrt{x+1}=5+3$

$2-\sqrt{x+1}=8$

Next, subtract two from both sides.

$2-\sqrt{x+1}=8$

_____________________

$-\sqrt{x+1}=6$

Now, divide both sides by negative one.

$\frac{-\sqrt{x+1}}{-1}=\frac{6}{-1}$

$\sqrt{x+1}=-6$

From here, square both sides.

$(\sqrt{x+1})^2=(-6)^2$

x+1=36

Next, subtract one from both side to solve .

x+1=36

______________

x=35

Lastly, check for extraneous solutions.

$2-\sqrt{x+1}=5+3$

$\\2-\sqrt{35+1}=8 \\2-\sqrt{36}=8 \\2-\pm6=8 \\2--6=8 \\2-+6=-4\neq8$

Since one of the values is a correct solution this verifies x=35 as a solution.

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

Study concepts, example questions & explanations for Common Core: High School - Algebra

All Common Core: High School - Algebra Resources

Example Questions

Example Question #21 : Reasoning With Equations & Inequalities

Example Question #22 : Reasoning With Equations & Inequalities

All Common Core: High School - Algebra Resources

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