# GRE Math : How to find the solution to an inequality with multiplication

## Example Questions

### Example Question #13 : Inequalities

Quantitative Comparison

Column A:

Column B:

The relationship cannot be determined from the information provided.

Quantity B is greater.

The quantities are equal.

Quantity A is greater.

The relationship cannot be determined from the information provided.

Explanation:

For quantitative comparison questions involving a shared variable between quantities, the best approach is to test a positive integer, a negative integer, and a fraction. Half of our work is eliminated, however, because the question stipulates that x > 0.  We only need to check a positive integer and a positive fraction between 0 and 1. Plugging in 2, we see that quantity A is greater than quantity B. Checking 1/2, however, we find that quantity B is greater than quantity A. Thus the relationship cannot be determined.

### Example Question #221 : Algebra

If –1 < n < 1, all of the following could be true EXCEPT:

|n2 - 1| > 1

n2 < n

(n-1)2 > n

16n2 - 1 = 0

n2 < 2n

|n2 - 1| > 1

Explanation:

### Example Question #5 : How To Find The Solution To An Inequality With Multiplication

(√(8) / -x ) <  2. Which of the following values could be x?

-1

All of the answers choices are valid.

-2

-3

-4

-1

Explanation:

The equation simplifies to x > -1.41. -1 is the answer.

Solve for x

Explanation:

### Example Question #11 : Inequalities

We have , find the solution set for this inequality.

Explanation:

### Example Question #2 : How To Find The Solution To An Inequality With Multiplication

Fill in the circle with either , , or symbols:

for .

The rational expression is undefined.

None of the other answers are correct.

Explanation:

Let us simplify the second expression. We know that:

So we can cancel out as follows:

### Example Question #2 : How To Find The Solution To An Inequality With Multiplication

Solve the inequality .

Explanation:

Start by simplifying the expression by distributing through the parentheses to .

Subtract  from both sides to get .

Next subtract 9 from both sides to get . Then divide by 4 to get  which is the same as .

### Example Question #22 : Inequalities

Solve the inequality .

Explanation:

Start by simplifying each side of the inequality by distributing through the parentheses.

This gives us .

Add 6 to both sides to get .

Add  to both sides to get .

Divide both sides by 13 to get .

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