# GMAT Math : Solving equations

## Example Questions

### Example Question #41 : Solving Equations

Solve for :

Explanation:

We need to isolate . Move all other terms to the right hand side of the equation:

Combine like terms:

### Example Question #42 : Solving Equations

Solve for the value of :

Explanation:

To solve this absolute value equation, we need to set the right side of the equation equal to a positive and negative version in order to calculate the two options for absolute value.

OR

OR

OR

OR

### Example Question #43 : Solving Equations

You are given the equations above. What is ?

Explanation:

We first solve each of the equations to find  and :

Therefore, .

### Example Question #44 : Solving Equations

You are given the following equation:

What is the value of  ?

Explanation:

First, we need to solve the provided equation for .

We want to find the value of . We can put the equation in this form by subtracting  from each side:

### Example Question #45 : Solving Equations

Solve .

or

or

or

Explanation:

Since we are solving an absolute value equation, , we must solve for both potential values of the equation:

1.)

2.)

Solving Equation 1:

Solving Equation 2:

Therefore, for  or

### Example Question #46 : Solving Equations

Solve for

Not enough information provided

Explanation:

In order to solve  for , we need to isolate  on one side of the equation:

### Example Question #47 : Solving Equations

Which of the following is a solution to the equation ?

Two of the other answers are correct.

Explanation:

In order to find values of  and  for which , we need to plug the values into the equation:

1.)  Correct

2.) Incorrect

3.)  Incorrect

4.)  Incorrect

Therefore, the only correct answer is

### Example Question #48 : Solving Equations

Solve for

Not enough information provided

Explanation:

In order to solve the equation for , we need to isolate  on one side of the equation:

Reducing the fraction,

### Example Question #49 : Solving Equations

Solve for  in the equation

Explanation:

### Example Question #50 : Solving Equations

Solve for  in the equation: