# Solve Algebra Homework: 7((45y+30)/14)+9y=225

• 939
In summary: A better way to do this is to use the "graphics" mode on your calculator which will show you how each number affects the other - much easier to see and remember. If you're still struggling, an algebra tutor might be a better option.
939

## Homework Statement

7((45y + 30)/14) + 9y = 225

45y + 30 + 18y = 450

Where did the 7 go? What was divided by 14?

I'm not sure how this part was done, I undertand how to get the rest though...

## Homework Equations

7((45y + 30)/14) + 9y = 225

## The Attempt at a Solution

I can get the rest, but I simply have no idea how this part was done (it was example in book). It appers to inverse 7/14 and multiply it by 9y, but I don't know why...

Last edited:
7((45y + 30)/14) + 9y = 225

Lets make that more readable: $$7\left ( \frac{45y+30}{14}\right )+9y=225$$ ... multiply everything by 14, divide everything by 7. i.e. multiply through by 2.

Simon Bridge said:
7((45y + 30)/14) + 9y = 225

Lets make that more readable: $$7\left ( \frac{45y+30}{14}\right )+9y=225$$ ... multiply everything by 14, divide everything by 7. i.e. multiply through by 2.

Thanks, the only thing I don't get is...

1) why it becomes 2. If you took 14 out of the denominator wouldn't it become (7)(1/14) = 7/14?

2) Why do you multiply everything, including 225, not simply (45y + 30)?

939 said:
Thanks, the only thing I don't get is...

1) why it becomes 2. If you took 14 out of the denominator wouldn't it become (7)(1/14) = 7/14?
7/14 = 1/2. One way to get rid of that 1/2 is to multiply both sides of the equation by 2.
939 said:
2) Why do you multiply everything, including 225, not simply (45y + 30)?

Because whatever you do to one side of an equation, you have to do also to the other side.

I have to do the same thing to both sides in order to keep the expression true.

i.e. if y+2=4 is true
then it is also true that 2y+4=8 (x2 all through)
and it is also true that y+4=6 (+2 to both sides)

But it is not true that 2y+4=4 (x2 to the LHS only).

We can do anything we want to the equation: so long as we do it to both sides, the expression remains true. Some things we can do are more useful than others - i.e. none of the above tells you what value of y makes the expression true.

If we subtracted 2 from both sides, though...

For your problem - you can find the solution by multiplying through by 14, then dividing through by 7. x14/7=x2 !

OR, you could expand out the brackets, then put the LHS over a common denominator...

Mark44 said:
7/14 = 1/2. One way to get rid of that 1/2 is to multiply both sides of the equation by 2.

Because whatever you do to one side of an equation, you have to do also to the other side.

Highly appreciated, Mark.

Simon Bridge said:
I have to do the same thing to both sides in order to keep the expression true.

i.e. if y+2=4 is true
then it is also true that 2y+4=8 (x2 all through)
and it is also true that y+4=6 (+2 to both sides)

But it is not true that 2y+4=4 (x2 to the LHS only).

We can do anything we want to the equation: so long as we do it to both sides, the expression remains true. Some things we can do are more useful than others - i.e. none of the above tells you what value of y makes the expression true.

If we subtracted 2 from both sides, though...

For your problem - you can find the solution by multiplying through by 14, then dividing through by 7. x14/7=x2 !

OR, you could expand out the brackets, then put the LHS over a common denominator...

Thanks Simon Bridge, got it!

No worries.

If you are seeing expressions like above then you've probably been doing algebra for some time and being puzzled by it suggests that you were taught by the "transferring numbers from one side to the other" approach - rules like "swap sides swap signs" that sort of thing. Not helpful when you get to more complicated expressions.

## 1. What is the first step in solving this algebraic equation?

The first step in solving this equation is to simplify the expression within the parentheses. This can be done by using the distributive property to multiply 7 by each term inside the parentheses. This will give us 315y+210.

## 2. How do I isolate the variable in this equation?

To isolate the variable, we need to get rid of any constants or coefficients that are attached to it. In this case, we can start by subtracting 210 from both sides of the equation. This will give us 315y=15. Then, we can divide both sides by 315 to get y=15/315 or y=1/21.

## 3. Can I check my answer to ensure it is correct?

Yes, you can always check your answer by plugging it back into the original equation. In this case, we would substitute y=1/21 for y in the equation and see if both sides are equal. If they are, then our answer is correct.

## 4. Are there any other methods for solving this equation?

Yes, there are other methods such as using the elimination method or substitution method. However, for this specific equation, the most efficient method is to use the distributive property and isolate the variable.

## 5. Can this equation be solved using a calculator?

Yes, this equation can be solved using a calculator by entering the expression on one side of the equation and the simplified answer on the other side. The calculator will then solve for the variable and give you the answer.

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