Statements Reasons
1. 3x - 7 = -4 1.
2. 3x - 7 + 7 = -4 + 7 2.
3. 3x + 0 = -4 + 7 3.
4. 3x + 0 = 3 4.
5. 3x = 3 5.
6. (1/3) 3x = 3 (1/3) 6.
7. (1/3) 3x = 1 7.
8. 1x = 1 8.
9. x = 1 9.
To understand how each statement is justified, let's go through each step:
1. Starting with the equation 3x - 7 = -4. The goal is to isolate the "x" term on one side of the equation.
2. Adding 7 to both sides of the equation, we get 3x - 7 + 7 = -4 + 7. This step cancels out the -7 on the left side.
3. Simplifying both sides of the equation, we have 3x + 0 = -4 + 7. The zero on the left side does not change the value of 3x.
4. Further simplification gives us 3x + 0 = 3. This is because -4 + 7 equals 3.
5. Since adding 0 to any number does not change its value, we have 3x = 3.
6. Now, we want to divide both sides of the equation by 3. This step is done to isolate the "x" term.
7. Dividing both sides by 3 gives us (1/3) 3x = 3 (1/3). The 3 on the right side can be expressed as a fraction 3 (1/3) or 10/3.
8. Simplifying the left side of the equation, we have (1/3) 3x = 10/3. On the left side, the factor of 3 cancels out, leaving us with x.
9. Therefore, we have 1x = 10/3 or x = 10/3.
To summarize, the series of steps mentioned above illustrate the process of solving the equation 3x - 7 = -4 and finding the value of x, which in this case is x = 10/3.