Chapter 6 Algebra Lesson 5 Solving Equations with

Chapter 6: Algebra Lesson 5: Solving Equations with Variables on Both Sides THEORY

Variables on Both Sides: Level 1 Method #1: Preferred 3 m = m + 5 -m -m 2 m = 2 5 2 m 5 2 = FIRST Ask yourself: Can I simplify on either side of the equal sign? Answer: NO! You must start by combining the m with the 3 m. To do this you must do the opposite of add m which is subtract m. What you do on one side you do on the other!

Variables on Both Sides: Level 1 Method #2: Long Haul 3 m = m + 5 -3 m 0 = -2 m +5 -5 -5 -5 = -2 m -2 -2 You could take the 3 m and combine it with the m on the right side of the equal sign… 5/-2 = m This took longer than last time!

Variables on Both sides of the equal sign Level 2: First Try 2 m – 3 = 5 m + 10 +3 +3 2 m -5 m = 5 m + 13 -5 m -3 = m = 13 -3 Note: We CAN’T simplify either side of the equal sign. We can start with any term since on both sides of the equal sign there is a variable and a number. I will start with the -3.

Variables on Both sides of the equal sign Level 2: Second Try 2 m – 3 = 5 m + 10 -2 m -3 = 3 m + 10 -13= 3 m 3 3 m = -13 3 Note: We can not simplify either side of the equal sign. We can start with any term since on both sides of the equal sign there is a variable and a constant. I will start with the 2 m. I could have started with the -3, 5 m, or 10.

Variables on Both sides of the equal sign Level 3: SIMPLIFY FIRST! 5 x + 1 – 2 x = 6 x + 4 3 x +1 -3 x = 6 x + 4 -3 x 1 -4 -3 3 = 3 x + 4 -4 = 3 x 3 x = -1 Note: We CAN Simplify on the Left side of the equal sign! Subtract the 2 x from the 5 x as they belong to the same family! The 6 x is not included as it is on the other side of the equal sign. After Simplifying we can start at any term.