1. Solve Equations With Variables on Both Sides
Section 1.5
Advanced Algebra 1

2. 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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3. Use Steps to Solve Equation:
-3x + 4 = 5x – 8
Get variables on same side of equation – use inverse operation (add 3x)
+3x x
4 = 8x - 8
Solve 2 step equation
12 = 8x
x = 3/2

4. Use Steps to Solve Equation: 2(x + 7) + 3 = 5x - 1
distribute
2x + 17 = 5x - 1
Combine like terms
-2x x
Get variables on same side – use inverse operation
17 = 3x - 1
Solve 2 step equation
18 = 3x
x = 6

5. Use Steps to Solve Equation: 4(1 – 2x) = 4 – 6x
Get rid of ( ) -- distribute
+8x x
Get variables on same side – use inverse operation (add 8x)
4 = 4 + 2x
Solve 2 step equation
0 = 2x
x = 0

6. Use Steps to Solve Equation:
9 + 5x = 5x + 9
Get variables on same side of equation – use inverse operation (subtract 5x)
-5x -5x
9 = 9
When solving, if you get a TRUE STATEMENT, then that means that any real number works.
Infinite Solutions

7. Use Steps to Solve Equation:
6x – 1 = 6x – 8
Get variables on same side of equation – use inverse operation (subtract 6x)
-6x x
-1 = - 8
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.
x = no solutions
The solution is no real numbers or empty set

8. 5) Solve 3 - 2x = 4x – 6 + 2x +2x 3 = 6x – 6 + 6 + 6 9 = 6x 6 6
Clear the fraction – multiply each term by the LCD
Simplify
Add 2x to both sides
Add 6 to both sides
Divide both sides by 6
Check your answer
3 - 2x = 4x – 6
+ 2x +2x
= 6x – 6
= 6x
or 1.5 = x

9. Solve the equation. Check your answer.
y = 0.7y – 0.3
1: Move variable to one side
y = 0.7y – 0.3
–0.3y –0.3y
2: add/subtract
= 0.4y – 0.3
3: Multiple/divide
= 0.4y
2 = y

10. 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 – a
C: Combine like terms
4 – 2a = – a
M: move variable to
One side
+2a a
= a

11. = a
= 12a
A: add/subtract
M: multiply/divide

12. Solve the equation. Check your answer.
D: Distributive Property
M: Move variable to one side
A: Add/subtract
3 = b – 1
4 = b

13. Solve the equation.
1. 2m – 6 + 4m = 12
ANSWER 3
2. 6a – 5(a – 1) = 11
ANSWER 6

14. 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

15. Solve the equation.
g – 2 + g = 16
ANSWER 2
b + 2(b – 4) = 47 11
ANSWER
3. –6 + 4(2c + 1) = –34 –4
ANSWER

16. (x – 6) = 12 2 3 24
ANSWER 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?
3 h
ANSWER