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

Example Questions

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

Solve for :

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

Solve for :

Assume  is positive.

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 #21 : Algebraic Concepts

Solve for :

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 #11 : Understand And Apply Concepts Of Equations

Solve for :

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

Solve for :

You my assume is positive.

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.

Take the positive square root of both sides:

,

the correct response.

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

Solve for :

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.