In order to solve this problem, we need to start at  on the number line. 

Next, we have  which means we need to move  places to the left on the number line. When we have an addition sign   we move to the right because that is towards the positive side of the number line. When we have a subtraction sign  we move to the left because that is towards the negative side of the number line. 

The orange arrow moved  places to the left, and ended at ; thus,

In order to solve this problem, we need to start at  on the number line. 

Next, we have  which means we need to move  places to the left on the number line. When we have an addition sign   we move to the right because that is towards the positive side of the number line. When we have a subtraction sign  we move to the left because that is towards the negative side of the number line. 

The orange arrow moved  places to the left, and ended at ; thus,

We know the following information:

In this particular case, do the negative numbers change our answer? There are a couple of rules that we need to remember when multiplying with negative numbers to help us answer this question:

• A negative number multiplied by a positive number will always equal a negative number
• A negative number multiplied by a negative number will always equal a positive number 

Thus,

The first step is to translate the words, "if  is added to  of another number, the result is ," into an equation. This gives us:

Subtract  from each side. 

Multiply each side by . 

Therefore,  is the correct answer. 

When adding and subtracting variable, you can only combine like variables.  

That means all of the  variables are solved separately from the  variables.  

Then you just add and subtract the constants normally so  and .  

So the final answer is .

When adding variables together, you must first make sure you are combining the same variable.  So, in this case

we can see that both terms contain the variable a.  Therefore, we can combine them. 

Now, when we combine them, we can think of the variables as objects.  So, we can say were are combining an apple and 4 apples together.  So,

We can simplify our problem the same way.

This problem is just a matter of grouping together like terms.  Remember that terms like  are treated as though they were their own, different variable:

The only part that might be a little hard is:

If you are confused, think of your number line.  This is like "going back" (more negative) from 15.  Therefore, you ranswer will be:

You need to begin by distributing the minus sign through the whole group .  This gives you:

Simplifying the double negative, you get:

Now, you can move the like terms next to each other:

Finally, simplify: