Equations with variables on both sides notes Absent Copy Thurs/Fri 2/21,22

1. Use G E M A (to simplify) on each side of the = sign. 2. Find the side of the = sign that has the smallest coefficient (#) w/the variable and do the inverse opp. and move it to the other side of the = sign. Ex: 3x + 4 = 6 + 5x -3x -3x 0 2x 3. Move the terms(inverse opp.) to one side of the = sign. 4. Use inverse opp. of mult./div. to get variable by itself to solve equation.

Example 1 Solve and check: 5a – 5 = 7 + 2a -2a -2a 3a 0 3a – 5 = a = 12 3 a = 4 Solution Is there any GEMA(simplifying) that needs to be done in this equation. YES or NO What is the smallest coefficient with the a. The 2 is the smallest number with the a What inverse opp. do we use to move the 2a. We use the inverse opp. Of addition and subtract 2a from both sides. What term do we move using the inverse opp. -5 or 7 Now what inverse opp. Do we use to solve for a. We use the inverse opp. Of mult. and divide by 3 on each side. a = 4

Example 2 Solve and check 4(x – 5) + 2 = x + 3 4x – = x + 3 4x – 18 = x x -x 3x 0 3x – 18 = = x = 21 3 x = 7 Solution What do we do with the 4 on the outside of the groupings? We have to use the distributive property. Do we have to use any GEMA to simplify? YES or NO What is the smallest coefficient with the x. The 1 is the smallest number with the x. What inverse opp. do we use to move the 1x. We have to use the inverse opp. of addition and subtract 1x from both sides. What term do we move using the inverse opp. -18 or 3 Now what inverse opp. Do we use to solve for x. We have to use the inverse opp. Of mult. And divide by 3 on both sides. X = 7