9514 1404 393
Answer:
left-to-right
- subtract 2y
- distribute 5
- add 2y
- divide by 25
Step-by-step explanation:
[There's a lot to read here. If you read it, maybe you'll have a better understanding.]
This is asking you the first step required to solve each of the equations.
The general process of solving an equation involves performing operations that result in the variable of interest being on one side of the equal sign (by itself), and everything else being on the other side. When variable and constant terms are mixed, we generally want to remove the variable term.
The underlying rule for all of this is "whatever is done to one side of the equation must also be done to the other side." The exceptions are simplification and substitution.
"Inverse" operations are of use in this process. That is why you are taught about the "additive inverse" (negative) of a number, and the "multiplicative inverse" (reciprocal) of a number. Adding the additive inverse results in the additive identity element (0). Similarly, multiplying by the multiplicative inverse results in the multiplicative identity element (1). Adding 0 or multiplying by 1 leaves only the original value.
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With this in mind, we can look at the given equations to see what is needed to solve them.
<u>2 +2y = y</u>
We see that the left side of the equation has both a constant term and a variable term. To remove the variable term we add its additive inverse: (-2y). Adding a negative value is the same as subtracting a positive value. That is, we can describe what we want to do as "subtract 2y from both sides".
When we do that, the result is ...
2 +2y -2y = y -2y . . . . . here, we show the subtraction
2 = -y . . . . . . . . . . . . . and this is the result of simplifying that.
Notice the y term is now on one side of the equal sign and the constant is on the other side. We are one step closer to the solution, which is the whole point.
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<u>5(y -4) = 2y</u>
This equation has parentheses. It often works well as a first step to eliminate the parentheses, generally using the distributive property. That is, we "distribute 5".
When we do that, the result is ...
5(y) -5(4) = 2y . . . . . . . . here, we show the distribution
5y -20 = 2y . . . . . . . and this is the result of simplifying that
This puts us one step closer to the solution, which is the whole point.
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<u>5y = 10 -2y</u>
Here, the unwanted variable term is -2y on the right side of the equation. To remove it, we add 2y to both sides.
When we do that, the result is ...
5y +2y = 10 -2y +2y . . . . . . . showing the addition of 2y
7y = 10 . . . . . . . . . . . . . . . simplified
This puts us one step closer to the solution.
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<u>5 = 25y</u>
This equation has the variable term and the constant term already separated. However, there is a coefficient on the variable term that is not equal to 1. We want to make that coefficient be 1. To do that, we multiply it by its multiplicative inverse: 1/25. That is, we divide both sides by 25.
When we do that, the result is ...
5/25 = 25y/25 . . . . . . showing division by 25
1/5 = y . . . . . . . . . simplified (and the fraction reduced)
This gives us the solution. There are no more steps required.
