SOLUTION: please help me understand how to answer this equation 2-5(x-3)=8

Question 448659: please help me understand how to answer this equation
2-5(x-3)=8
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given to solve for x:
2-5(x-3)=8
There are several sequences that can be used to solve this equation. I'll show you one set of steps that will get the answer.
Remember that in general the object is to get the variable x on one side of the equal sign and all the numbers on the other side.
Notice that the x is inside a set of parentheses. So, for the time being, we keep the parentheses on the left side and get the numbers on the right side.
Let's begin by getting rid of the number 2 on the left side. We can do this by subtracting 2 from both sides of the given equation. When we subtract two from the left side, the number 2 disappears. The subtraction of 2 from the left side means that we need to subtract 2 from the right side also. The right side becomes 8 - 2 or just 6 and we are left with:
-5(x-3) = 6
Next, multiply -5 on the left side by each term in the parentheses. The -5 times x equals -5x and the -5 times -3 becomes +15. When we make these substitutions the equation becomes:
-5x + 15 = 6
Now we get rid of the number +15 on the left side by subtracting 15 from both sides. When we do that the number 15 disappears from the left side, and the number on the right side is 6 - 15 = -9. So the equation becomes:
-5x = -9
To get rid of the minus signs on both sides, we may choose to multiply both sides by -1. When we do, the equation becomes:
5x = 9
We want to know what x (or 1x) equals. Since the left side is 5x we can change it to x (or 1x) by dividing it by 5. When we do this we must also divide the right side by 5. The result is:
x = 9/5
That's the answer. For convenience and simplification we can divide out the right side ... that is we can divide 9 by 5 and get 1.8 for the answer. So we have the answer:
x = 1.8
Let's check the answer by substituting 1.8 for x in the original problem. When we do, the left side of the problem is:
2 - 5(1.8 - 3)
Combine the two terms in the parentheses (1.8 - 3) to find that this is -1.2. Substitute -1.2 for the quantity in the parentheses:
2 - 5(-1.2)
Multiply -5 times -1.2 and you get +6. So when x is 1.8 the left side of the problem becomes:
2 + 6
Note that this is +8 and it is equal to the right side of the equation in the given problem. Therefore, x = 1.8 is the solution to your problem.
You can play around with the problem and find other sequences that will work to arrive at the same answer. For example, you could begin by multiplying -5 times each of the terms in the parentheses to make the left side of the equation become:
2 -5x + 15
combine the 2 and the +15 to get +17 and the left side becomes:
-5x + 17
Set this equal to the right side to get:
-5x + 17 = 8
Subtract 17 from both sides to get rid of the number 17 from the left side.
-5x = 8 - 17
Combine the two numbers on the right side:
-5x = -9
Note that this is the same as we got before. Dividing both sides by -5 results in:
x = -9/-5 = 9/5 = 1.8
Again, this is the same answer that we got previously.
Hope this helps you to understand the problem and the fact that there may be more than one way to solve it. Just follow the general rules for solving equations and the rules for combining numbers algebraically.

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