# GMAT Math : Linear Equations, One Unknown

## Example Questions

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### Example Question #1 : Solving Linear Equations With One Unknown

For what value of  would the following equation have no solution?

The equation must always have at least one solution regardless of the value of  .

Explanation:

Simplify both sides of the equation as much as possible, and solve for  in the equation in terms of :

has exactly one solution unless the denominator is 0 - that is, . We make sure that this value renders no solution by substituting:

The equation has no solution, and  is the correct answer.

Solve for :

Explanation:

Solve for :

Explanation:

Solve for :

Explanation:

### Example Question #5 : Solving Linear Equations With One Unknown

What is the midpoint coordinate of  and ?

Explanation:

Midpoint formula:

### Example Question #6 : Solving Linear Equations With One Unknown

What is the midpoint coordinate of and ?

Explanation:

Midpoint formula:

### Example Question #7 : Solving Linear Equations With One Unknown

What is the midpoint coordinate of  and ?

Explanation:

Midpoint formula:

### Example Question #8 : Solving Linear Equations With One Unknown

Solve the following equation:

.

Explanation:

We start by isolating the absolute value expression:

This gives us two cases when we remove the absolute value:

and

Then we solve for each case:

### Example Question #1 : Linear Equations, One Unknown

Solve for :

The equation has no solution.

Explanation:

Solve for :