To solve the equation for x, simplify.

To remove the absolute value, we do the following:

From there, we simplify both equations until we are left with x by itself on the left side.

There, you have the solutions for x.

To solve the expression, simply plug in the given value for x. 

1. 

2. 

3. 

4. 

5. 

Note: at step 1, don't forget that squaring a negative number yields a positive number, because (-) * (-) = (+), while cubing a negative number yields a positive number, because (+) * (-) = (-).

Remember, when a question says something like "h as a function of t", it means that h is dependent on the value of t. This means the equation would take the form y=mx+b, and h would take the place of y, the dependent variable, while t would take the place of x, the independent variable. This eliminates answer choices that have t in the dependent variable spot and h in the independent variable spot.

Next, the value for m in our new equation, h=mt+b, would be the rate of change (also known as the slope). The rate of change we're given in the problem is 30 feet per minute (the feet per minute tells you that this is a rate of change).

Finally, the value for b is the y-intercept (or in our case, the h-intercept). It is the starting value for our equation (when t = 0). The starting value we're given in the problem is 17 feet.

Therefore, the correct equation to model the hot air balloon is

Before we simplify the expressions, let's determine any restrictions that may be in place. Restrictions are where the denominator equals 0. Our expression has  as the denominator. The denominator equals 0 when , so we know we have at least one restriction at .

Now, we can simplify the expression. First, we factor the numerator.

Now, our expression is this:

Therefore, our expression simplifies to . There are no more restrictions in place with the simplified version, so the only restrictions we have are that . Our answer is 

To express this situation we would have the following general form.

For our case, let  be the price of each pen, which is the unknown.

Then, since we bought  pens, the cost of  pens would be .

Additionally, we spent  on the candy bar.

The total cost of the purchase was .

Usually the total is by itself on one side of the equals sign.

Thus, we have that the equation is . 

The equation must be set up so that the amount saved is dependent upon total income, ; Joe will set aside 5% of the money he makes for savings. We represent this algebraically as:

Next, we see that no matter how much money Joe makes, he plans to always set aside $65 per month for savings. This is called a constant because it doesn't matter how his total income varies, the $65 remains constant. We complete the expression for Joe's savings with this constant term, leaving us with:

The above expression is equivalent to Joe's savings, which we represent with the variable , so we create our equation:

The relationship can be described using multiplication by a factor of 2 (i.e. twice Patrick's age) and subtraction by 5 (i.e. 5 years less); the subtraction does not take place inside of parentheses because it is Matt's age that is 5 years less and not Patrick's (which is represented by the variable ). Therefore, the equation describing the relationship between the brothers' ages is:

The dollar amount is .  Pennies are , and quarters are .  Two equations will need to be used to solve for the amount of pennies and quarters to make up the dollar.

The first equation sums up the total of coins used.  The total of pennies and quarters must add up to 35 coins.

The second equation uses the denominations of the pennies and quarters that sum up to the dollar.  Write the equation.

These are the two equations needed to solve for .

The answer is:

To set up this equation, we must break down the statement into parts.

Let  be the number.

Twice a number:  

Is:  

Two less than the number:  

Combine the parts.

The answer is:  

In order to set up this equation,  we will need to break up the sentence statement into parts.  Let the unknown number be .

Three times a number:  

Is:  

Two less than twice the number:  

Combine the parts together.

The correct answer is: