# Tutor profile: Christine A.

## Questions

### Subject: Pre-Algebra

Solve $$ 4(x+6)+2(3x-5) $$.

To solve this, we work from left to right in the equation. The first step is to distribute the $$4$$ to what is inside of the parenthesis. To do this, we first multiply $$4$$ by $$x$$, and then we multiply $$4$$ by $$6$$. So the first part of the equation becomes $$4(x)+4(6)$$. Next we simplify the equation. We cannot simplify $$4x$$ beyond what we have already done, because we do not know what the variable $$x$$ means here, so it stays as $$4x$$. However, we can simplify $$4(6)$$: $$4$$ times $$6$$ is $$24$$. So the first part of the equation is $$4x+24$$. The same thing we did to the first part of this equation, we do to the second part of the equation as well. Remember that the equation, although it looks like $$3x-5$$, it is actually $$3x+(-5)$$. Now we multiply $$2$$ by $$3x$$, and we multiply $$2$$ by $$-5$$. $$2$$ times $$3x$$ becomes $$6x$$. $$2$$ times $$-5$$ is $$-10$$. So the second part of the equation becomes $$6x+(-10)$$. To simplify that even more, it becomes $$6x-10$$. Now we combine what we did to find the final answer. $$4x+24$$ plus $$6x-10$$. This equation becomes $$4x+24+6x-10$$. Now we combine like terms - any terms that have $$x$$ in it can be combined, and any terms that that are normal numbers can also be combined. Here, we have two terms that have an $$x$$: $$4xx$$ and $$6x$$. So these terms can be added together: $$4x+6x$$, which becomes $$10x$$. We also have two numbers that can be added together: $$24$$ and $$-10$$. This equation becomes $$24+(-10)$$, which is $$24-10=14$$. Now we bring it all together to find the final answer: $$10x+14$$. So the answer to the question asking us to solve $$ 4(x+6)+2(3x-5) $$ is $$10x+14$$.

### Subject: English

Please provide an example of a metaphor and an example of a simile.

A metaphor is a figure of speech that compares one thing to another, but the sentence does not use the words "like" or "as". An example is: "She is a couch potato." A simile is similar to a metaphor, but the main difference is that it uses the words "like" or "as". An example is "She ran like the wind."

### Subject: Algebra

What is the inverse of the function $$ f(x)=x^2+4 $$?

When you see a question that asks you to find the inverse to a function, the easiest thing to do is to switch the variables around. It sounds more complicated than it is. Remember that $$ f(x) $$ is just another way to say "y" in an equation. So putting that understanding in, the question is asking what the inverse of $$ y=x^2+4 $$ is. Now that we know what is "x" and "y" here, remember that an inverse means to switch the variables. So to find the inverse of the equation that they gave us, switch around the "x" and "y" variables. When you switch those variables around, the equation becomes $$ x=y^2+4 $$. Now, like most other algebra equations, we solve for y. To solve for "y", you have to get "y" by itself. So the first thing we can do is subtract 4 from each side - we want to do that so that we can start to get the "y" variable by itself, and whatever we do to one side of an equation we have to do to the other side as well. So when we subtract 4 from both sides, we get $$ x-4=y^2 $$. In the equation, we see that "y" is squared. To finish the problem and get "y" by itself, we have to find the square root of "y". And remember, what we do to one side of an equation, we have to do to the other as well. So we have to find the square root of both sides of the equation. That leaves us with the answer: $$ \sqrt{x-4}=y $$. Remember, "y" is another way to say $$ f(x) $$. To signify a function is the inverse of another, we use the term $$ f^{-1}(x) $$ [and the original function remains $$ f(x) $$]. So the answer is $$ \sqrt{x-4}=f^{-1}(x) $$. To put it in an order that is more familiar, the answer is $$ f^{-1}(x)=\sqrt{x-4} $$.

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