Solve Equations With Variables on Both Sides
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Transcript 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