Download Unit 1 Day 1: Solving One- and Two

UNIT 1 DAY 3: SOLVING EQUATIONS
WITH VARIABLES ON BOTH SIDES
ESSENTIAL QUESTIONS: How do we
solve equations with variables on both
sides? When does an equation have no
solution or a solution of all real numbers?
SOLVING EQUATION RULE
Any change applied to one side of an equation
must be applied to the other side in order to
keep the balance.
What you do to one side
you must do to the other side
SOLVING EQUATIONS WITH VARIABLES ON BOTH SIDES
Step 1: Draw a line straight down from the equal sign to
separate the left side from the right.
Step 2: Simplify each side separately.
Step 3: Use inverse operations to collect the variables on
one side of the equation and the constants on the other
side of the equation.
Step 4: Solve using the steps from Day 1 & 2.
Step 5: Check your answer by plugging it back into the
original equation and simplifying.
Example 1: Solve the equations.
a)
7x + 19 = -2x + 55
+ 2x
+ 2x
9x + 19 = 55
- 19 -19
9x = 36
9
9
x=4
b)
6x + 22 = 3x + 31
- 3x
- 3x
3x + 22 = 31
- 22 -22
3x = 9
3
3
x=3
Example 2: Solve the equations.
a)
80 – 9y = 6y
+ 9y
+ 9y
80
15
80
15
16
3
= 15y
15
=y
=y
b)
10c = 24 + 4c
- 4c
6c
6
- 4c
= 24
6
c=4
Example 3: Solve the equation.
4(1 – x) + 3x = -2(x + 1)
4 - 4x + 3x
= -2x - 2
4 - 1x
+ 2x
= - 2x - 2
+ 2x
4+x =-2
-4
-4
x = -6
Example 4: Solve the equation.
9(n – 4) – 7n = 5(3n – 2)
9n - 36 - 7n = 15n - 10
2n - 36
- 15n
-13n - 36
+ 36
-13n
-13
= 15n - 10
- 15n
= - 10
+ 36
= 26
-13
n = -2
EQUATIONS WITH NO SOLUTION OR A SOLUTION
OF ALL REAL NUMBERS
Happens when the variable is eliminated and you are left with a
true or false statement.
True Statement
False Statement
Example: 5 = 5
Example: 5 = 2
All Real Numbers
(any number substituted for
the variable will work)
No Solution
(no number substituted for
the variable will work)
Example 5: Solve the equations (True or False).
a)
x - 2x + 3 = 3 - x
-x + 3 = 3 - x
+x
+x
3 =3
true statement
all real numbers
b)
5x + 24 = 5(x - 5)
5x + 24 = 5x - 25
- 5x
- 5x
24 = -25
false statement
no solution
Example 6: Phone Company A charges an activation fee of 36 cents and
then 3 cents per minute. Phone Company B charges 6 cents per minute with
no activation fee. How long is a call that costs the same amount no matter
which company is used?
If you talk for 12
minutes, it will not
matter which
company you use.
.36 + .03x = .06x
- .03x - .03x
.36 = .03x
.03 .03
12 = x
Example 7: Justin and Tyson are beginning an exercise program to train for
football season. Justin weighs 150 pounds and hopes to gain 2 pounds per
week. Tyson weighs 195 pounds and hopes to lose 1 pound per week. If the
plan works, in how many weeks will the boys weigh the same amount?
Justin
In 15 weeks,
Justin and Tyson
will weigh the
same amount.
150 + 2x
Tyson
= 195 - 1x
+ 1x
+ 1x
150 + 3x = 195
- 150
- 150
3x = 45
x = 15
SUMMARY
Essential Questions: How do we solve equations
with variables on both sides? When does an
equation have no solution or a solution of all
real numbers?
Take 1 minute to write 2 sentences answering the
essential questions.