What is the answer to 2a plus 8 equals 5a-3?

Answer 1

Well our first goal should be to write the equation.

1. 2a + 8 = 5a - 3

Now our second goal is to get the variable (a) all to one side and all the numbers to one side. In Algebra it is most common to see the variable on the left and numbers on the right. However in this case, we'd be smarter moving the numbers to the left since they hold a positive value. (+3 + 8 = + 11). If we moved it the other way we'd be dealing with a negative value and those complicate things.

1. 2a + 8 = 5a - 3
2. 2a + 8 + 3 = 5a - 3 + 3
3. 2a + 11 = 5a

Now our third goal is to get the variable to the right. Even though we'll be subtracting - the value of the variables coefficient will remain positive.

1. 2a + 11 = 5a
2. 2a - 2a + 11 = 5a - 2a
3. 11 = 3a

Now our final step is to remove the attached variable. If you notice the (a) is being multiplied to the 3. So we need to perform the opposite or inverse operation which is division.

1. 11 = 3a
2. 11/3 = 3a/3
3. 3 2/3 = a

So now that we have the value of A - A rule in Algebra is to always double check to verify your solution is correct. Let's do this by plugging the value of a, which is 3 2/3, into the original equation.

1. 2a + 8 = 5a - 3
2. 2 (3 2/3) + 8 = 5 (3 2/3) - 3

Let's do the left side first to determine it's value.

1. 2 (3 2/3) + 8 =
2. 7 1/3 + 8 = 15 1/3

Now we know that the left side equated to 15 1/3 - So in order for our solution to be correct the right side now has to equal 15 1/3. Let's calculate it.

1. 5 (3 2/3) - 3 =
2. 18 1/3 - 3 = 15 1/3

So there we have it. Both sides of the original equation are equaled when A = 3 2/3.