Answer:
See below
Explanation:
How to solve equations algebraically
To solve equations algebraically, your main goal is to get the variable on one side of the equal sign while getting the constant on the other side of the equal sign.
Its important to remember that
- Variables are typically represented by a letter such as "x" or "b"
- Constant are simply numbers such as 11 or -9
How to move variables and constants to the other side:
We can change the position of a variable/constant regarding which side of the sign it is on by using inverse operations. For example if we have 2x = 7 + x. We would want to get the x on the other side, we can do this by doing the inverse of adding an x which would be subtracting an x. So we would subtract x , but whatever we do to one side we must to do the other, so we would subtract x from both sides resulting us in getting 2x - x = 7 + x - x which simplifies to x = 7.
Remember these are the operations inverses
We have
- Addition is inverse subtract vise versa
- Division is inverse multiplication vise versa
- Square roots are inverse exponents vise versa
( There are some other ones but these are the three main ones )
What are like terms?
Like terms are terms with the same variable and degree. An example of like terms would be 2x and 7x or 8b and 20b. When we see like terms in an equation we combine them ( add them together ). Note that this is only when the like terms are on the same side of the equal sign.
Applying what we just learned to find the answer
We have the equation 24b - 10b = 126
==> First step is to combine like terms 24b and -10b ( 24b - 10b = 14b)
14b = 126
==> next step is to get rid of the "14" on b. 14 is being multiplied by b. The inverse of multiplication is division so to get rid of the 14 we would divide by 14 but whatever we do to one side we must do to the other so we divide both sides by 14. ( 14b / 14 = b and 126 / 14 = 9 )
we are left with b = 9