For algebraic problems, the key is to get the variable (b, in the case of your example) all by itself on one side of the equals sign. (The variable is kind of a loner like that.) However, whatever you do to one side of the equals sign must be done to the other side.
In general, a good method for getting the variable by itself is to do order of operations backwards until the variable is left alone on one side. So start with addition and subtraction. In this case, we have an added 34 on the side of the variable. To get this to go away, we subtract 34 (the opposite operation, as an above poster mentioned). However, we have to do that to both sides. This leaves us with: 12b = 33
Next, we multiply and divide. We have a multiplied 12 on the side of the variable, so we do the opposite operation (dividing 12) to both sides of the equation. This leaves us with b = 33/12. You can reduce this fraction by dividing both the top (numerator) and bottom (denominator) by their greatest common factor (in this case, 3). This leaves b = 11/4
Now, b is all by itself on one side of the equals sign. We have solved the equation for b!
As a review of what we did with this example, here is another similar problem:
3x - 7 = 14
3x - 7 + 7 = 14 + 7
3x = 14 + 7
3x = 21
3x/3 = 21/3
x = 21/3
x = 7
I hope this helps you better understand algebra in the future!
If you find it hard to wrap your head around all this math, sometimes it helps to think of it in terms of a real-life situation. If you understood already, or if word problems confuse you, then don't bother reading this next part. However, if you are still having trouble and prefer word problems, thinking of algebra in the context of a word problem can help. For example, for your problem (12b + 34 = 67)... you can imagine that you are buying some candy from a friend. He offers to give you 12 pieces of candy and 34 cents in you give him 67 cents. You know how much one piece of candy costs, and want to make sure you are getting a fair deal, so you need to find out how much you are paying for each piece of candy. Why pay him 67 cents if he is giving you 34 cents? Instead, he could keep his 34 cents and you could pay him an addition 33 cents, leaving him with the same amount of money (67 cents) that he wanted. Now you know you are paying 33 cents for 12 candies, but how much is that per candy? 33 cents per 12 candies is 33/12 of a cent per candy, which reduces to 11/4 cent. If candy costs 3 cents per piece (12/4 of a cent), then you are making a good deal. However, if it only costs 2 cents a piece (8/4 of a cent), you are not making a good deal. If the word problem confused you more than helped you, then feel free to think of it in the original way. I'm just trying to offer up alternate ways of going about the same problem.
Comments
For algebraic problems, the key is to get the variable (b, in the case of your example) all by itself on one side of the equals sign. (The variable is kind of a loner like that.) However, whatever you do to one side of the equals sign must be done to the other side.
In general, a good method for getting the variable by itself is to do order of operations backwards until the variable is left alone on one side. So start with addition and subtraction. In this case, we have an added 34 on the side of the variable. To get this to go away, we subtract 34 (the opposite operation, as an above poster mentioned). However, we have to do that to both sides. This leaves us with: 12b = 33
Next, we multiply and divide. We have a multiplied 12 on the side of the variable, so we do the opposite operation (dividing 12) to both sides of the equation. This leaves us with b = 33/12. You can reduce this fraction by dividing both the top (numerator) and bottom (denominator) by their greatest common factor (in this case, 3). This leaves b = 11/4
Now, b is all by itself on one side of the equals sign. We have solved the equation for b!
As a review of what we did with this example, here is another similar problem:
3x - 7 = 14
3x - 7 + 7 = 14 + 7
3x = 14 + 7
3x = 21
3x/3 = 21/3
x = 21/3
x = 7
I hope this helps you better understand algebra in the future!
If you find it hard to wrap your head around all this math, sometimes it helps to think of it in terms of a real-life situation. If you understood already, or if word problems confuse you, then don't bother reading this next part. However, if you are still having trouble and prefer word problems, thinking of algebra in the context of a word problem can help. For example, for your problem (12b + 34 = 67)... you can imagine that you are buying some candy from a friend. He offers to give you 12 pieces of candy and 34 cents in you give him 67 cents. You know how much one piece of candy costs, and want to make sure you are getting a fair deal, so you need to find out how much you are paying for each piece of candy. Why pay him 67 cents if he is giving you 34 cents? Instead, he could keep his 34 cents and you could pay him an addition 33 cents, leaving him with the same amount of money (67 cents) that he wanted. Now you know you are paying 33 cents for 12 candies, but how much is that per candy? 33 cents per 12 candies is 33/12 of a cent per candy, which reduces to 11/4 cent. If candy costs 3 cents per piece (12/4 of a cent), then you are making a good deal. However, if it only costs 2 cents a piece (8/4 of a cent), you are not making a good deal. If the word problem confused you more than helped you, then feel free to think of it in the original way. I'm just trying to offer up alternate ways of going about the same problem.
Again, I hope this helped!
12b + 34 = 67
First subtract 34 from both sides of the equation:
12b = 33
Now divide both sides by 12 to get b on it's on own:
b = 33/12 (which can also be written as 2 3/4)
so first in your equation you need to take out all the things that are the same and try to cancel them so subtract the 35 from the 67 so
12b + 34 =67
-34 -34
12b = 33
so now you have that but you are looking for the value of b so you should divide by the coeffienct of b which is the number in front of it or 12 so
12b = 33
----- ------
12 12
is b = 33/12 =2 and 3/4th
Subtract 34 from LHS and RHS of the equation.
12b + 34 - 34 = 67 - 34
12b = 33
Now, divide both sides by 12
12b / 12 = 33/ 12
b = 33 / 12
Hope this helped
there is a simple rule to do this.
when ever u send any value after '=' symbol it changes opposite
like +x becomes -x after = symbol
-x becomes +x
*x becomes /x
/x becomes *x
here we have 12b+34 = 67
send +32 to other side it becomes -32... so 12b = 67 -32=35
send 12 to other side then it will become division
b =(67-32) /12
=35/12