GMAT Math : Solving linear equations with one unknown

Example Questions

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

What is the midpoint coordinate of  and ?

Explanation:

Midpoint formula:

Example Question #6 : Linear Equations, One Unknown

What is the midpoint coordinate of and ?

Explanation:

Midpoint formula:

Example Question #7 : Linear Equations, One Unknown

What is the midpoint coordinate of  and ?

Explanation:

Midpoint formula:

Example Question #8 : Linear Equations, 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 #9 : Linear Equations, One Unknown

Solve for :

The equation has no solution.

Explanation:

Solve for :