Question

Solve for b.

9(b-a)=r

Answer 1

`b=(r)/(9)+a`

Explanation:

Main Concepts:

Concept 1. Solving for a variable

Concept 2. Undoing a multi-step equation

Concept 1. Solving for a variable

To solve any equation ever in mathematics, there are two main steps:

• Step 1. Get the variable to appear exactly once
• Step 2. Isolate the variable

In this case, the variable already appears exactly once, so we can skip ahead to Step 2.

Concept 2. Undoing a multi-step equation

To "Isolate the variable", one must undo the things that are done to it.

To undo something, things must be undone in the reverse order in which they are done.

Looking at the equation, "b" appears on the left side of the equation. Focusing on the left side, if everything were a number and we were trying to simplify it, Order of Operations would require us to take the "b" and do the following:

1. subtract by "a" in the parentheses

2. then multiply by 9

To undo these things, we'll need to use the opposite operation of what would have been done in the first place.

• Multiplication and Division are opposites
• Addition and Subtraction are opposites

To undo the steps above, we undo them in reverse order, so

1. Undo multiplication by 9

2. Then undo the subtraction by "a".

`9(b-a)=r`

To undo the multiplication, divide both sides by 9

`(9(b-a))/(9)=(r)/(9)`

simplifying the left side gives

`b-a=(r)/(9)`

To undo the subtraction by "a", add "a" to both sides

`b-a+a=(r)/(9)+a`

simplifying the left side gives

`b=(r)/(9)+a`

Answer 2

`b=(r)/(9) +a`

Explanation:

To solve this problem, we have to isolate b. The steps are shown below:

Given -
`9(b-a)=r`

Divide both sides by 9 -
`(9(b-a))/(9)=(r)/(9)` →
`(b-a)=(r)/(9)`

Add a to both sides -
`(b-a+a)=(r)/(9)+a` →
`b=(r)/(9) +a`

So after doing these steps, we are left with our answer of
`b=(r)/(9) +a`.