Justifying Steps to Solving Equations
Ch. 1
Day #9
Warm Up - Solve each
1) 5x + 5 = 3(5x – 4) – 10x
2) 3(2b – 1) – 7 = 6b – 10
Justification of Solving Equations using Properties
3) Consider the equation 3(x + 2) – 2(x + 7) = 4x + 7. The steps in solving the equation are shown below.
Justify each step.
Step 1: 3x + 6 – 2x – 14 = 4x + 7
Justification:______________________________________
Step 2: 3x – 2x + 6 – 14 = 4x + 7
Justification:______________________________________
Step 3: x – 8 = 4x + 7
Justification:______________________________________
Step 4: -x + x – 8 = 4x + 7 – x
Justification:______________________________________
Step 5: -8 = 4x + 7 – x
Justification:______________________________________
Step 6: -8 = 4x – x + 7
Justification:______________________________________
Step 7: -8 = 3x + 7
Justification:______________________________________
Step 8: -7 – 8 = 3x + 7 – 7
Justification:______________________________________
Step 9: -15 = 3x
Justification:______________________________________
Step 10: (1/3)(-15) = (3x)(1/3)
Justification:______________________________________
Step 11: -5 = x
Justification:______________________________________
4) Consider the equation
Step 1:
5∙
−2(𝑥−3)
5
−2(𝑥−3)
5
= 4. The steps to solving are shown. Justify each step.
= 4∙5
Justification:______________________________________
Step 2: -2(x – 3) = 20
Justification:______________________________________
Step 3: -2x + 6 = 20
Justification:______________________________________
Step 4: -2x + 6 – 6 = 20 – 6
Justification:______________________________________
Step 5: -2x = 14
Justification:______________________________________
Step 6: (-1/2)(-2x) = (14)(-1/2)
Justification:______________________________________
Step 7: x = -7
Justification:______________________________________
5) Solve the equation and justify each step.
5x – 3(x + 1) = 2(x + 4)