### All GMAT Math Resources

## Example Questions

### Example Question #41 : Solving Equations

Solve for :

**Possible Answers:**

**Correct answer:**

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 :

**Possible Answers:**

**Correct answer:**

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 ?

**Possible Answers:**

**Correct answer:**

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 ?

**Possible Answers:**

**Correct answer:**

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 .

**Possible Answers:**

or

or

**Correct answer:**

or

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 :

**Possible Answers:**

Not enough information provided

**Correct answer:**

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 ?

**Possible Answers:**

Two of the other answers are correct.

**Correct answer:**

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 :

**Possible Answers:**

Not enough information provided

**Correct answer:**

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

**Possible Answers:**

**Correct answer:**

### Example Question #50 : Solving Equations

Solve for in the equation:

**Possible Answers:**

**Correct answer:**