# GMAT Math : Solving equations

## Example Questions

### Example Question #21 : Solving Equations

Give the solution set of the equation:

Explanation:

Case 1:

Then , and the equation becomes

Case 2:

Then , and the equation becomes

However, this conflicts with the fact that , so this is a false solution.

The only solution is therefore .

### Example Question #22 : Solving Equations

Give the solution set of the equation:

Explanation:

Case 1:  is nonnegative - that is, .

The equation becomes

Either , in which case ,

or , in which case , which is impossible, as we are assuming that  is nonnegative.

case 2:  is negative - that is,

The equation becomes

Either , in which case , which is impossible since we are assuming that  is negative,

or , in which case .

and  can both be confirmed as solutions.

### Example Question #23 : Solving Equations

What is the equation of the line that goes through  and is parallel to ?

Explanation:

First, we have to find the slope from  using the general form  Therefore

Parallel lines have the same slope, so the new line has a slope of  and point .

Use the point-slope equation:

### Example Question #24 : Solving Equations

What is the -intercept of ?

Explanation:

To solve for the -intercept, you set the  to zero and solve for :

-intercept:

### Example Question #25 : Solving Equations

What is the y-intercept of ?

Explanation:

To solve for the y-intercept, you set  to zero and solve for :

Therefore, the y-intercept is:

### Example Question #26 : Solving Equations

What is the -intercept of ?

Explanation:

To solve for the -inter, you set  to zero and solve for :

x-intercept:

### Example Question #27 : Solving Equations

What is the y-intercept of ?

Explanation:

To solve for the y-intercept of , you set  to zero and solve for :

y-intercept:

### Example Question #341 : Algebra

To convert Fahrenheit temperature  to the equivalent in Celsius , use the formula

To the nearest tenth of a degree, convert  to degrees Celsius.

Explanation:

### Example Question #342 : Algebra

Solve for :

The equation has no solution.

Explanation:

Rewrite as a compound equation, then solve each equation individually:

or

### Example Question #343 : Algebra

Solve for :

The equation has no solution.

Explanation:

Eliminate the denominators by multiplying by , then solve the resulting equation:

Solve using the  method:

or

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