To solve for the variable we must move all constants to the other side of the equation. Since we have absolute value bars in the particular equation we will first move all constants that are outside of the absolute value bars. To do this apply the oppisite operation. In this particular case, subtract twelve from both sides.

Now we will deal with the absolute value bars which state that the quantity inside them can be positive of negative.

Either

or .

Solve each separately:

 Therefore, or .

The correct choice is  .

To solve for the variable we must move all constants to the other side of the equation. Since we have absolute value bars in the particular equation we will first move all constants that are outside of the absolute value bars. To do this apply the oppisite operation. In this particular case, subtract 125 from both sides.

or

Solve separately:

To figure out the total portraits done by James, you must multiply rate  by the number of months .  This equation would be .  To solve for the number of months  you must divide both sides by . This gives us .

The first step is to simplify your equation.  You distribute  to get .  Then to get  by itself you add  to both sides ending with .  Finally insert the -coordinate to get  which equals .

To get  by itself, divide each side by  to get .  Then add  to both sides to get .

The absolute value of a nonnegative number is the number itself; the absolute value of a negative number is its positive opposite.

By substitution, 10.5 can be seen to be a solution of each of the equations in the five choices. For example:

 - a true statement.

That 10.5 is a solution of the other four equations can be proved similarly. Therefore, the question is essentially to choose the equation with  as its other solution. Again, we can do this using substitution in each equations. We see that  is correct as follows:

 - a true statement.

Similar substitution in the other four statements shows that  is not a solution of any of them; for example, in :

 - a false statement.

Convert  to the Celsius scale by setting  in the conversion formula and solving for :

The question is therefore asking for the number of days that the temperature topped . Examine the graph below:

The high temperature was greater than  on Tuesday, Friday, and Saturday - three different days.

Tommy's current age is represented by t, and Sara's is represented by s. In five years, both Tommy's and Sara's ages will be increased by five. Thus, in five years, we can represent Tommy's age as and Sara's as .

The problem tells us that Tommy's age in five years will be twice as great as Sara's in five years. Thus, we can write an algebraic expression to represent the problem as follows:

In order to solve for t, first simplify the right side by distributing the 2.

Then subtract 5 from both sides.

The answer is .

In order to solve this, we need to set up an equation. , where  is time. All we need to do is divide by  on each side.

First we need to create equations that represent the path's of the Rocket's.

For Rocket , the equation is

For Rocket , the equation is

In order to solve for the time the Rocket's cross, we need to set the equations equal to each other.

Now solve for