Download Solve Equations With Variables on Both Sides

Solve Equations With
Variables on Both Sides
Section 1.5
Advanced Algebra 1
Steps to Solve Equations
with Variables on Both Sides
1) Simplify each side

Get rid of double Negatives
Get rid of fractions

Distribute

Combine Like Terms
 2) Move variables to same side

“Smaller to the bigger”
 3) Solve by using INVERSE Operations
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
Use Steps to Solve Equation:
-3x + 4 = 5x – 8
+3x
+3x
4 = 8x - 8
+8
+8
12 = 8x
8
8
x = 3/2
Get variables on same side
of equation – use inverse
operation (add 3x)
Solve 2 step equation
Use Steps to Solve Equation:
2(x + 7) + 3 = 5x - 1
2x + 14 + 3 = 5x – 1
2x + 17 = 5x - 1
-2x
-2x
17 = 3x - 1
+1
+1
18 = 3x
3
3
x= 6
distribute
Combine like terms
Get variables on same side –
use inverse operation
Solve 2 step equation
Use Steps to Solve Equation:
4(1 – 2x) = 4 – 6x
4 – 8x = 4 - 6x
+8x
+ 8x
4 = 4 + 2x
-4 -4
0 = 2x
2
2
x= 0
Get rid of ( ) -- distribute
Get variables on same side
– use inverse operation
(add 8x)
Solve 2 step equation
Use Steps to Solve Equation:
9 + 5x = 5x + 9
-5x -5x
9=9
Infinite
Solutions
Get variables on same side
of equation – use inverse
operation (subtract 5x)
When solving, if you get a
TRUE STATEMENT, then
that means that any real
number works.
Use Steps to Solve Equation:
6x – 1 = 6x – 8
-6x
-6x
-1 = - 8
x = no solutions
The solution is no real
numbers or empty set
Get variables on same side
of equation – use inverse
operation (subtract 6x)
The variables zeroed out
and remaining is a false
statement where a
number is equal to a
different number, so there
will be no number that will
work in the equation.
3 1
1
3
x
=
x
5) Solve 8 4
2
4
1.
2.
3.
4.
5.
6.
7.
8.
9.
Clear the fraction – multiply
each term by the LCD
Simplify
Add 2x to both sides
Simplify
Add 6 to both sides
Simplify
Divide both sides by 6
Simplify
Check your answer
3
1
1
3
(8) - (8) x = (8) x - (8)
8
4
2
4
3 - 2x = 4x – 6
+ 2x +2x
3
= 6x – 6
+6
+6
9
= 6x
6
6
3
or 1.5 = x
2
3 1
1
3
 1.5  1.5 
8 4
2
4
Solve the equation. Check your answer.
0.5 + 0.3y = 0.7y – 0.3
0.5 + 0.3y = 0.7y – 0.3
–0.3y –0.3y
0.5
= 0.4y – 0.3
+0.3
+ 0.3
0.8
= 0.4y
2=y
1: Move variable to one side
2: add/subtract
3: Multiple/divide
Simplifying Each Side Before
Solving Equations
4 – 6a + 4a = –1 – 5(7 – 2a)
D: Distributive P.
4 – 6a + 4a = –1 –5(7 – 2a)
4 – 6a + 4a = –1 –5(7) –5(–2a)
4 – 6a + 4a = –1 – 35 + 10a
4 – 2a = –36 + 10a
+2a
+2a
4
= -36 + 12a
C: Combine like
terms
M: move variable to
One side
4
+ 36
40
= -36 + 12a
A: add/subtract
+36
= 12a
M: multiply/divide
Solve the equation. Check your answer.
D: Distributive Property
M: Move variable to one side
3=b–1
+1
4=b
+1
A: Add/subtract
Solve the equation.
1. 2m – 6 + 4m = 12
ANSWER
3
2. 6a – 5(a – 1) = 11
ANSWER
6
Create an equation, then solve the equation.
3. A charter bus company charges $11.25 per ticket
plus a handling charge of $.50 per ticket, and a $15
fee for booking the bus. If a group pays $297 to
charter a bus, how many tickets did they buy?
ANSWER
24 tickets
Solve the equation.
1.
8g – 2 + g = 16
ANSWER
2.
2
3b + 2(b – 4) = 47
ANSWER
11
3. –6 + 4(2c + 1) = –34
ANSWER
–4
4.
2 (x – 6) = 12
3
ANSWER
24
5. Joe drove 405 miles in 7 hours. He drove at a rate of 55
miles per hour during the first part of the trip and 60
miles per hour during the second part. How many hours
did he drive at a rate of 55 miles per hour?
ANSWER
3h