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

## Example Questions

### Example Question #12 : Inequalities

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

n2 < n

(n-1)2 > n

n2 < 2n

16n2 - 1 = 0

|n2 - 1| > 1

|n2 - 1| > 1

Explanation:

### Example Question #13 : Inequalities

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

-3

-2

All of the answers choices are valid.

-4

-1

-1

Explanation:

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

Solve for x

Explanation:

### Example Question #4 : How To Find The Solution To An Inequality With Multiplication

We have , find the solution set for this inequality.

Explanation:

### Example Question #28 : Inequalities

Fill in the circle with either , , or symbols:

for .

None of the other answers are correct.

The rational expression is undefined.

Explanation:

Let us simplify the second expression. We know that:

So we can cancel out as follows:

### Example Question #1 : How To Find The Solution To An Inequality With Multiplication

What is the greatest value of  that makes

a true statement?

Explanation:

Find the solution set of the three-part inequality as follows:

The greatest possible value of  is the upper bound of the solution set, which is 277.

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

What is the least value of  that makes

a true statement?

Explanation:

Find the solution set of the three-part inequality as follows:

The least possible value of  is the lower bound of the solution set, which is 139.

### Example Question #3 : How To Find The Solution To An Inequality With Multiplication

Give the solution set of the inequality:

None of the other responses gives the correct answer.

Explanation:

Divide each of the three expressions by , or, equivalently, multiply each by its reciprocal, :

or, in interval form,

.

### Example Question #4 : How To Find The Solution To An Inequality With Multiplication

Give the solution set of the following inequality:

None of the other responses gives the correct answer.

Explanation:

or, in interval notation, .

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

Which of the following numbers could be a solution to the inequality ?