SOLVING EQUATIONS WITH VARIABLES ON BOTH SIDES
Algebra 1: 3.4 SOLVING EQUATIONS WITH VARIABLES ON BOTH SIDES
Goal: Get ONE variable alone on one side of = sign.
1. Use Distributive Property, if necessary.
2. Combine like terms, if necessary
3. Move one variable by adding its inverse to both sides of =.
4. Solve as usual.
|[pic] |Original problem |
| |Move variables to one side. |
| | |
| |Eliminate adding or subtracting |
| |Eliminate multiplying or dividing |
| |Solution! Remember…Check Your Answer! |
|[pic] |Original Problem |
| |Do the Distributive Property First!!! |
| |Move Variables to one Side. |
| | |
| |Eliminate adding or subtracting |
| |Eliminate multiplying or dividing |
| |Solution! Remember…Check Your Answer! |
|[pic] |Original Problem |
| |Do the Distributive Property First!!! |
| |Combine Like Terms |
| |Move Variables to one Side. |
| |Eliminate adding or subtracting |
| |Eliminate multiplying or dividing |
| |Solution! Remember…Check Your Answer! |
Try These!!!
4. 5x = -7x + 6 5. 7 – 3x = x – 4(2 + x)
HMMM……..Take a look at the following examples:
6. [pic] 7. [pic]
The Rules:
• When you solve an equation and you end with a true statement, the solution set will be: _______________________.
|[pic] |
|[pic] |
|- 3x - 3x |
|[pic] |
Example:
Many Solutions!
• When you solve an equation and you end with a false statement, the solution set will be: _______________________.
|[pic] |
|[pic] |
|- 3x - 3x |
|[pic] |
No Solutions!
Try These:
8. 2x + 5 = 2x – 3 9. 3(x+1) – 5 = 3x – 2
Class Practice:
10. 6x + 7 = 8x – 13 11. 6(y + 2) – 4 = -10
12. 4(2x – 8) = 3(2 – 3x) 13. 4(r + 20) = 1/5(20r + 400)
14. -2x = -3x + 12 – 2x 15. 8(b + 1) + 4 = 3(2b – 8) – 16
Algebra 1: 3.4 Solving Equations Homework
Solve the Equation. Show all Steps!!!
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More On Back
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