About Solving Literal Equations:

When we work with formulas, we often have to solve for one of the variables involved. In order to accomplish this task, we isolate that variable on one side of the equation, using our normal four-step process.


Test Objectives
  • Demonstrate the ability to solve an equation for a specified variable
Solving Literal Equations Practice Test:

#1:

Instructions: solve each equation for the given variable.

$$a)\hspace{.2em}F=\frac{9}{5}C + 32,\hspace{.2em}» \hspace{.2em}C$$

$$b)\hspace{.2em}d=rt,\hspace{.2em}» \hspace{.2em}t$$


#2:

Instructions: solve each equation for the given variable.

$$a)\hspace{.2em}C=\frac{5}{9}\left(F - 32\right),\hspace{.2em}» \hspace{.2em}F$$

$$b)\hspace{.2em}V=LWH,\hspace{.2em}» \hspace{.2em}H$$


#3:

Instructions: solve each equation for the given variable.

$$a)\hspace{.2em}A=\frac{1}{2}bh,\hspace{.2em}» \hspace{.2em}h$$

$$b)\hspace{.2em}A=2xy^2 + 2xyz,\hspace{.2em}» \hspace{.2em}x$$


#4:

Instructions: solve each equation for the given variable.

$$a)\hspace{.2em}y - y_{1}=m(x - x_{1}),\hspace{.2em}» \hspace{.2em}x$$

$$b)\hspace{.2em}y=\frac{-az - b}{xz},\hspace{.2em}» \hspace{.2em}z$$


#5:

Instructions: solve each equation for the given variable.

$$a)\hspace{.2em}yz + m=\frac{z + 4}{x - 1},\hspace{.2em}» \hspace{.2em}z$$

$$b)\hspace{.2em}m^2x - a^2x=\frac{z + b - x}{y + 1},\hspace{.2em}» \hspace{.2em}x$$


Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}C=\frac{5}{9}(F - 32)$$

$$b)\hspace{.2em}t=\frac{d}{r}$$


#2:

Solutions:

$$a)\hspace{.2em}F=\frac{9}{5}C + 32$$

$$b)\hspace{.2em}H=\frac{V}{LW}$$


#3:

Solutions:

$$a)\hspace{.2em}h=\frac{2A}{b}$$

$$b)\hspace{.2em}x=\frac{A}{2y(x + z)}$$


#4:

Solutions:

$$a)\hspace{.2em}x=\frac{y - y_{1}}{m}+ x_{1}$$

$$b)\hspace{.2em}z=-\frac{b}{xy + a}$$


#5:

Solutions:

$$a)\hspace{.2em}z=\frac{-xm + m + 4}{xy - y - 1}$$

$$b)\hspace{.2em}x=\frac{z + b}{-a^2y + m^2y + m^2 - a^2 + 1}$$