Lesson 10A
RCSD Geometry Local Curriculum
Name:__________________________
U1
Period:_______ Date:____________
Lesson 10A: Solving Literal Equations
or ….. Variables everywhere!! SOLVING LINEAR EQUATIONS WITH UNSPECIFIED CONSTANTS
Learning Target: I can solve equations with unspecified constrains
Opening Activity
a. Solve for the value of 𝑥.
5𝑥 + 3 = 33
b. Solve for the value of 𝑥. Write your answer in
terms of the unspecified constants 𝑎, 𝑏, and 𝑐.
𝑎𝑥 + 𝑏 = 𝑐
What is the difference between equation (a) and (b)?
__________________________________________________________________________________________
__________________________________________________________________________________________
Example 2.
Solve the following two equations for 𝑥. In (b), leave your answer in terms of the constants 𝑎, 𝑏, 𝑐 and 𝑑.
Example 3. Solve both equations below for 𝑥
𝑎. 8𝑥 + 1 = 5𝑥 + 22
b. 𝑎𝑥 + 𝑏 = 𝑐𝑥 + 𝑑
U1
Lesson 10A
RCSD Geometry Local Curriculum
Name:__________________________
Period:_______ Date:____________
Literal Equations: equations with _________ than _________ ________________ .
When the literal equation is expressing a relationship that exists in the real-world (i.e. area, distance, volume)
we call it a ________________________
Examples of _____________________:
𝐹 = 𝑚𝑎
𝐷 = 𝑟𝑡
𝑃𝑣 = 𝑛𝑟𝑇
5
𝐶 = 9 (𝐹 − 32)
REMEMBER~


Variables are placeholders for numbers and as such have the same properties.
When solving an equation with several variables, you use the same properties and reasoning as with
single variable equations.
Examples of formulas we know: 𝐷 = 𝑅𝑇 or 𝐷 =
𝑀
𝑉
or 𝐴 = 𝐿𝑤 or 𝑃 = 2𝐿 + 2𝑤
 Our goal when working with these types of equations is to be able to solve them for any
variable that appears in it.
Example 3
For what variable is the equation 𝑠 =
Solve 𝑠 =
𝑑
𝑡
for variable 𝑑 instead:
𝑑
𝑡
solved for? ____________
𝑑 = ________________
When solving equations with unknown constraints (literal equations) or “Transforming Formulas” we to solve
the formula for one of the variables that is not typically isolated in the equation. We do this by using inverse
operations with the other numbers/variables in the equation.
Example 4
a) Solve for 𝑡:
𝑑 =𝑡∙𝑟
b) Solve for 𝑉 in terms of 𝑀 and 𝐷:
D
M
V
Lesson 10A
RCSD Geometry Local Curriculum
Name:__________________________
c) Solve for 𝐿 in terms of 𝑃 and 𝑊:
P  2L  2W
U1
Period:_______ Date:____________
d)
Solve for 𝑤
𝐴 = 𝐿𝑤
Example 5
The area 𝐴 of a rectangle is 25 in2. The formula for area is 𝐴 = 𝐿𝑤
Rearrange the area formula to solve for 𝐿 in order to help you solve the above problem:
L
a) If the width 𝑤 is 10 inches, what is the length 𝐿? __________
𝐴 = 25 𝑖𝑛2
w
b) If the width 𝑤 is 15 inches, what is the length 𝐿? ___________
Example 6
The perimeter formula for a rectangle is 𝑝 = 2(𝑙 + 𝑤) where 𝑝 represents the perimeter, 𝑙 represents the
length, and 𝑤 represents the width. Calculate 𝑙 when 𝑝 = 70 and 𝑤 = 15.
Lesson 10A
RCSD Geometry Local Curriculum
Name:__________________________
U1
Period:_______ Date:____________
Lesson 10A: Solving Literal Equations
Problem Set
1. Solve for c.
p
bc
5
4. Solve for s. 20 x  5s  8
2. Solve for m.
t
vm
3
5.
3. Solve for h.
A
1
bh
2
6.
Solve for b.
Solve for h.
16c  10b  2
A
1
(b1  b2 ) h
2