# SAT Math : How to find the solution to an equation

## Example Questions

### Example Question #91 : How To Find The Solution To An Equation

.

Which of the following is a solution of this equation?

Explanation:

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  .

### Example Question #92 : How To Find The Solution To An Equation

Give the solution set to this equation.

or

or

or

or

The equation has no solution.

or

Explanation:

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:

### Example Question #93 : How To Find The Solution To An Equation

James is an artist and makes  number of portraits per month.  At this rate, how many months will it take him to paint  portraits?

Explanation:

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 .

### Example Question #94 : How To Find The Solution To An Equation

Point  lies on the line with the equation .  If the -coordinate for  is , what is the -coordinate?

Explanation:

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 .

### Example Question #95 : How To Find The Solution To An Equation

If , then  is equal to what?

Explanation:

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

### Example Question #96 : How To Find The Solution To An Equation

Which of the following equations has as its solution set  ?

Explanation:

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.

### Example Question #241 : New Sat

Above is a graph which gives the high and low temperatures, in degrees Celsius, over a one week period for Washington City. Temperature given in degrees Celsius can be converted to the Fahrenheit scale using the following formula, where  and  are the temperature expressed in degrees Celsius and degrees Fahrenheit, respectively:

On how many days of the week shown on the graph did the temperature get above ?

Three

Five

Four

Six

Seven

Three

Explanation:

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.

### Example Question #51 : How To Find The Solution To An Equation

Tommy's and Sara's current ages are represented by t and s, respectively. If in five years, Tommy will be twice as old as Sara, which of the following represents t in terms of s?

Explanation:

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.

### Example Question #97 : How To Find The Solution To An Equation

If Billy runs at a pace of , how long will it take billy to run ?

Explanation:

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.

### Example Question #91 : Linear / Rational / Variable Equations

Rocket  is launched from the ground at , and Rocket  is launched  off the ground at . At what time will Rocket  and Rocket  cross path's?

Explanation:

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