Transcript What is a literal equation? - St Lucie County School Sites

Objective:
Solve literal equations for a specified variable
Benchmark Number: MA.8.A.4.1
The process of solving a formula for a given variable is
called "solving literal equations". One of the dictionary
definitions of "literal" is "related to or being comprised
of letters", and variables are sometimes referred to as
literals. So "solving literal equations" is a fancy way of
saying "taking an equation with lots of letters, and
solving for one letter in particular.“
Literal equations are often used to solve real world
problems. Such as…….
Rules to solve literal equations
1.
Simplify each side of the equation, if needed, by distributing or
combining like terms.
2.
Move the variable being solved for to one side of the equation by
using the opposite operation of addition or subtraction.
3.
Isolate the variable being solved for by itself by applying the
opposite operation to each side.
a. First, use the opposite operation of addition or
subtraction to move any other constants or variables to
the other side.
b. Second, use the opposite operation of multiplication or
division to eliminate the coefficient of the variable
being solved for.
Let’s solve the following literal equation:
2x – 4y = 7 Solve for x
Step One:
Simplify: Ask yourself, “Do I need to combine any like
terms on both sides of this literal equation?
a) Yes
b) No
Let’s solve the following literal equation:
2x – 4y = 7 Solve for x
Step Two:
Next, to get x by itself; what do you need to
move to both sides?
a) Add 2x
b) Subtract 2x
c) Add 4y
d) Subtract 4y
2x – 4y = 7 Solve for x
Third, let’s use a “Do/Undo” chart to determine what to
do next.
Ask yourself…….
• What do you need to do to
isolate X?
• What is the second thing?
DO
UNDO
Subtract 4y
Add 4y
Multiply 2
Divide 2
* Remember to follow the steps in
the UNDO column to isolate the
variable
Solve for x
1.
2.
3.
4.
5.
Draw the “River”
Add 4y to both sides
Simplify
Divide both sides by 2
Does it simplify?
2x - 4y = 7
+ 4y
2x
2
x
= + 4y
= 7 + 4y
= 2
= 7 + 4y
2
* This fraction cannot be
simplified because both
terms in the numerator
are not divisible by 2.
Let’s solve the following literal equation:
2x – 4y = 7 Solve for y
Step One:
Simplify: Ask yourself, “Do I need to combine any like
terms on both sides of this literal equation?
a) Yes
b) No
Let’s solve the following literal equation:
2x – 4y = 7 Solve for y
Step Two:
Next, to get x by itself; what do you need to
move to both sides?
a) Add 2x
b) Subtract 2x
c) Add 4y
d) Subtract 4y
2x – 4y = 7 Solve for y
Third, let’s use a “Do/Undo” chart to determine what to
do next.
Ask yourself…….
• What do you need to do to
isolate y?
• What is the second thing?
DO
UNDO
Add -2x
Subtract -2x
Multiply -4
Divide -4
* Remember to follow the steps in
the UNDO column to isolate the
variable
Solve for y
1. Draw the “River”
2. Subtract 2x from both
sides
3. Simplify
4. Divide both sides by -4
5. Does it simplify?
NO!!!!
2x - 4y = 7
- 2x
-4y
-4
y
= - 2x
= 7 – 2x
= -4
= 7 - 2x
-4
A thing is obviously mathematical
after you see it so just remember….
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