Literal Equations

Literal Equations

What are literal equations??

Any equation with more than one variable is a literal equation.

They look like this:

How do we solve them?

Just like solving 1 variable equations we will use inverse (opposite) operations until we get the variable that we want by itself.

Multiple Choice

REVIEW: Which inverse operation would you use to solve the following equation for x.

$$x+5=11$$

• Addition

• Subtraction

• Multiplication

• Division

Multiple Choice

REVIEW: Which inverse operation would you use to solve the following equation for x.

$$x-4=16$$

• Addition

• Subtraction

• Multiplication

• Division

Multiple Choice

REVIEW: Which inverse operation would you use to solve the following equation for x.

$$3x=56$$

• Addition

• Subtraction

• Multiplication

• Division

Multiple Choice

REVIEW: Which inverse operation would you use to solve the following equation for x.

$$\frac{x}{2}=27$$

• Addition

• Subtraction

• Multiplication

• Division

Now let's solve a literal equation!

Multiple Choice

Solve for x: $$x-y=z$$

• $$x=\frac{z}{y}$$

• $$x=z+y$$

• $$x=z-y$$

• $$x=zy$$

Multiple Choice

Solve for x: $$xy=z$$

• $$x=\frac{z}{y}$$

• $$x=z+y$$

• $$x=z-y$$

• $$x=zy$$

Multiple Choice

Solve for x: $$\frac{x}{y}=z$$

• $$x=\frac{z}{y}$$

• $$x=z+y$$

• $$x=z-y$$

• $$x=zy$$

What if there are 2 terms to move?

Multiple Choice

Solve for y. $$y+em=w$$

HINT: When variable are multiplied (combined) you can move them together

• $$y=w-em$$

• $$y=w+em$$

• $$y=\frac{w}{em}$$

• $$y=wem$$

Multiple Choice

Solve for h. $$V=lwh$$

HINT: When variable are multiplied (combined) you can move them together

• $$h=Vlw$$

• $$h=\frac{l}{Vw}$$

• $$h=\frac{w}{lV}$$

• $$h=\frac{V}{lw}$$

Match

Solve the equation PV=nRT for each variable.

• P=

• V=

• n=

• R=

• T=

• $$\frac{nRT}{V}$$

• $$\frac{nRT}{P}$$

• $$\frac{PV}{RT}$$

• $$\frac{PV}{nT}$$

• $$\frac{PV}{nR}$$

Labeling

REVIEW: Label the correct order of operations to solve the equation for x.

(HINT: Think the opposite of PEMDAS)

Drag labels to their correct position on the image

Divide both sides by 5

Add 3 to both sides

Multiple Choice

Solve for a: $$2a+b=c$$

• $$2a=c-b$$

• $$a=2\left(c-b\right)$$

• $$a=\frac{c-b}{2}$$

• $$a=\frac{c+b}{2}$$

Multiple Choice

Solve for y: $$am+xy=c$$

• $$y=\frac{c-am}{x}$$

• $$y=\frac{c+am}{x}$$

• $$y=c-amx$$

• $$y=\frac{c-x}{am}$$

Multiple Choice

Solve for x: $$p=ax+g$$

• $$x=ap+g$$

• $$x=\frac{p-g}{a}$$

• $$x=\frac{p+g}{a}$$

• $$x=ap-g$$

Multiple Choice

Solve for y: $$2y-4x=16$$

• $$y=2x+8$$

• $$y=-2x+8$$

• $$y=-4x+16$$

• $$y=4x+16$$

Match

Match each equation by solving for y.

• 6x+2y=12

• -5x+5y=15

• 2y-6x=18

y=-3x+6

y=x+3

y=3x+9

• y=-3x+6

• y=x+3

• y=3x+9