One and Two Step Equations and Inequalties
Inverse Operations 5 + 12 = 17 -12 = -12 5 = 5 These are operations that undo each other. For Example: I get back to 5 by subtracting what I added. 5 + 12 = 17 -12 = -12 5 = 5
Inverse Operations What is the opposite/inverse of multiplication? What is the opposite/inverse of addition? What is the opposite/inverse of subtraction? What is the opposite/inverse of division? Division Subtraction Addition Multiplication
Isolating the Variable - When you get the variable all by itself. X = -3
Type 1: -3x + 10 = 1 - 10 -10 -3x + 0 = -9 -3 -3 x = 3 You need to get x all by itself! -3x + 10 = 1 Get rid of the adding or subtracting FIRST! - 10 -10 Do the Opposite! -3x + 0 = -9 Now get rid of the multiplication or division! -3 -3 Do the Opposite! x = 3
You try: -2x + 12 = 2 - 12 -12 -2x + 0 = -10 -2 -2 x = 5 Get rid of the adding or subtracting FIRST! - 12 -12 Do the Opposite! -2x + 0 = -10 Now get rid of the multiplication or division! -2 -2 Do the Opposite! x = 5
Type 2: You need to get y all by itself! y 2 - 4 = 12 Get rid of the adding or subtracting FIRST! +4 +4 Do the Opposite! y 2 Now get rid of the multiplication or division! 2● +0 = 16 ●2 Do the Opposite! y = 32
You Try: y 3 - 5 = 4 Get rid of the adding or subtracting FIRST! +5 +5 Do the Opposite! y 3 Now get rid of the multiplication or division! 3● +0 = 9 ●3 Do the Opposite! y = 27
Type 3: 2 5 - - x = -4 2 5 -5● x = -4 ●-5 - 2x = 20 2 2 x = 10 Bring the negative up or down 2 5 - - x = -4 2 5 Now get rid of the division! -5● x = -4 ●-5 Do the Opposite! - 2x = 20 Now get rid of the multiplication! 2 2 Do the Opposite! x = 10
You Try: 3 7 - - x = -3 3 7 -7● x = -3 ●-7 - 3x = 21 3 3 x = 7 Bring the negative up or down 3 7 - - x = -3 3 7 Now get rid of the division! -7● x = -3 ●-7 Do the Opposite! - 3x = 21 Now get rid of the multiplication! 3 3 Do the Opposite! x = 7
Type 1: You need to get a all by itself! Get rid of the adding or subtracting FIRST! 5 – a = 6 - 5 -5 Do the Opposite! -a = 1 Now get rid of the NEGATIVE SIGN! -1 -1 Divide by -1 a = -1
You Try: -3 – x = 15 +3 +3 -x = 18 -1 -1 x = -18 You need to get x all by itself! Get rid of the adding or subtracting FIRST! -3 – x = 15 +3 +3 Do the Opposite! -x = 18 Now get rid of the NEGATIVE SIGN! -1 -1 Divide by -1 x = -18
Type 2: -x – 12 = 15 +12 +12 -x +0 = 27 -1 -1 x = -27 You need to get x all by itself! -x – 12 = 15 Get rid of the adding or subtracting FIRST! +12 +12 Do the Opposite! Now get rid of the NEGATIVE SIGN! -x +0 = 27 Divide by -1 -1 -1 x = -27
You Try: -x + 8 = -1 -8 -8 -x +0 = -9 -1 -1 x = 9 You need to get x all by itself! -x + 8 = -1 Get rid of the adding or subtracting FIRST! -8 -8 Do the Opposite! Now get rid of the NEGATIVE SIGN! -x +0 = -9 Divide by -1 -1 -1 x = 9
Type 3: You need to get x all by itself! Get rid of the adding or subtracting FIRST! 8 + 2x = -2 - 8 -8 Do the Opposite! 2x = -10 Now get rid of the Multiplication! 2 2 Do the Opposite x = -5
You Try: -3 - 6x = -21 +3 +3 -6x = -18 -6 -6 x = 3 You need to get x all by itself! Get rid of the adding or subtracting FIRST! -3 - 6x = -21 +3 +3 Do the Opposite! -6x = -18 Now get rid of the Multiplication! -6 -6 Do the Opposite x = 3
Solve & then graph the inequality. Let's Try: 1 2 3 4 5 -1 -2 -3 -4 -5 -6 6
Solve & then graph the inequality. You Try: 1 2 3 4 5 -1 -2 -3 -4 -5 -6 6
Solve & then graph the inequality. Let's Try: 1 2 3 4 5 -1 -2 -3 -4 -5 -6 6
Solve & then graph the inequality. You Try: 1 2 3 4 5 -1 -2 -3 -4 -5 -6 6
Solve & then graph the inequality. Let's Try: When multiplying or dividing by a negative you must FLIP the sign. 1 2 3 4 5 -1 -2 -3 -4 -5 -6 6
Solve & then graph the inequality. You Try: When multiplying or dividing by a negative you must FLIP the sign. 1 2 3 4 5 -1 -2 -3 -4 -5 -6 6
Solve & then graph the inequality. You Try: When multiplying or dividing by a negative you must FLIP the sign. 1 2 3 4 5 -1 -2 -3 -4 -5 -6 6