©Powered Chalk LLC 2009 Title slide

   x x x +0 Step 1- Undo addition or subtraction by using opposite operations on both sides of the equation. Divide by 3 on both sides. Step 2- Undo multiplication or division by using opposite operations, again to both sides of the equation. Subtract 2 to both sides. Our goal is to undo all the operations being done to the x. 2 makes the equation true. 3(2) + 2 = 8 Invisible 1 ©Powered Chalk LLC 2009 Ex. 1 ( 3x + 2 = 8 )

   x x x +0 Step 1- Undo addition or subtraction by using opposite operations on both sides of the equation. Divide by 5 on both sides. Step 2- Undo multiplication or division by using opposite operations, again to both sides of the equation. Add 2 to both sides. Our goal is to undo all the operations being done to the x. 2 makes the equation true. 5(2) - 2 = 8 Invisible 1 ©Powered Chalk LLC 2009 Ex. 2 ( 5x - 2 = 8 )

16 4/3x4/3x 12 ¾ ¾    x x x +0 invisible 1 Step 1- Undo addition. Multiply both sides of the = by 4 / 3. Step 2- Undo multiplication by a fraction by multiplying by the reciprocal. Subtract 5 from both sides of the = Undo all the operations being done to the x. 16 makes the equation true. ¾ (16) + 5 = 17 X 4/3X 4/3 ©Powered Chalk LLC 2009 Ex. 3 ( 3 / 4 x + 5 = 17)

33 3/2x3/2x 22 2/32/ /32/3    x x x +0 invisible 1 Step 1- Undo subtraction. Multiply both sides by 3/2. Step 2- Undo multiplication by a fraction by multiplying by the reciprocal. Add 5 to both sides. Undo all the operations being done to the x 33 makes the equation true. 2 / 3 (33) - 5 = 17 X 3/2X 3/2 ©Powered Chalk LLC 2009 Ex. 4 ( 2 / 3 x -5 = 17

   x x x 0 invisible 1 Step 1- Undo subtraction. Divide by -3 on both sides of = Step 2- Undo multiplication. Add 2 to both sides of the =. Undo all the operations being done to the x. -4 makes the equation true (-4) = 10 ©Powered Chalk LLC 2009 Ex. 5 ( -2 – 3x = 10)

   x x x 0 invisible 1 Step 1- Undo the addition. Divide by -3 on both sides. Step 2- Undo multiplication. Subtract 2 from both sides. Undo all the operations being done to the x. -3 makes the equation true (-3) = 11 Remember if there isn’t a sign in front of a number it is +. + ©Powered Chalk LLC 2009 Ex. 6 ( 2 – 3x = 11 )

3 x3x    - x x 0 Step 1- Undo the addition. Step 2- Undo division. Undo all the operations being done to the x. -15 makes the equation true. 15 = 10 – (-15)/3  3x 3x Step 3- Take the opposite sign of each side.  x -15 Remember if there isn’t a sign in front of a number it is +. + Subtract 10 from both sides of the =. Multiply both sides of = by 3. Step 4- Switch the x and -15.  x invisible 1 x ©Powered Chalk LLC 2009 Ex. 7 ( 15 = 10 – x/3 )

2 x2x    - x x Step 1- Undo the addition. Step 2- Undo division. Undo all the operations being done to the x. 30 makes the equation true. -5 = 10 – (30)/2  2x 2x Step 3- Take the opposite sign of each side.  x 30 + Subtract 10 from both sides of the =. Multiply both sides of = by 2. Step 4- Switch the x and 30.  x 30 2 invisible 1 x ©Powered Chalk LLC 2009 Ex. 8 ( -5 = 10 – x/2 )