HiSET: Math : Rearrange formulas/equations to highlight a quantity of interest

Study concepts, example questions & explanations for HiSET: Math

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Example Questions

Example Question #1 : Rearrange Formulas/Equations To Highlight A Quantity Of Interest

Solve for :

Possible Answers:

Correct answer:

Explanation:

To solve for  in a literal equation, use the properties of algebra to isolate  on one side, just as if you were solving a regular equation. 

Multiply both sides by :

Subtract  from both sides:

Multiply both sides by , distributing on the right:

,

the correct response.

 

Example Question #2 : Rearrange Formulas/Equations To Highlight A Quantity Of Interest

Solve for :

Assume  is positive.

Possible Answers:

Correct answer:

Explanation:

To solve for  in a literal equation, use the properties of algebra to isolate  on one side, just as if you were solving a regular equation. 

Subtract  from both sides:

Divide both sides by 9:

Take the square root of both sides:

Simplify the expression on the right by splitting it, and taking the square root of numerator and denominator:

,

the correct response.

Example Question #1 : Rearrange Formulas/Equations To Highlight A Quantity Of Interest

Solve for :

Possible Answers:

Correct answer:

Explanation:

To solve for  in a literal equation, use the properties of algebra to isolate  on one side, just as if you were solving a regular equation. 

First, take the reciprocal of both sides:

Multiply both sides by :

Distribute on the right:

Subtract 1 from both sides, rewriting 1 as to facilitate subtraction:

,

the correct response.

 

Example Question #4 : Rearrange Formulas/Equations To Highlight A Quantity Of Interest

Solve for :

Possible Answers:

Correct answer:

Explanation:

To solve for  in a literal equation, use the properties of algebra to isolate  on one side, just as if you were solving a regular equation. 

Subtract 20 from both sides:

Divide both sides by :

,

the correct response.

Example Question #2 : Rearrange Formulas/Equations To Highlight A Quantity Of Interest

Solve for :

You my assume is positive.

Possible Answers:

Correct answer:

Explanation:

To solve for  in a literal equation, use the properties of algebra to isolate  on one side, just as if you were solving a regular equation. 

First, add  to both sides:

Take the positive square root of both sides:

,

the correct response.

Example Question #6 : Rearrange Formulas/Equations To Highlight A Quantity Of Interest

Solve for :

Possible Answers:

Correct answer:

Explanation:

To solve for  in a literal equation, use the properties of algebra to isolate  on one side, just as if you were solving a regular equation. 

First, square both sides to eliminate the radical symbol:

Rewrite the expression on the right using the square of a binomial pattern:

Subtract 1 from both sides:

,

the correct response.

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