### All PSAT Math Resources

## Example Questions

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

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

**Possible Answers:**

(n-1)^{2} > n

16n^{2} - 1 = 0

n^{2} < n

n^{2} < 2n

|n^{2} - 1| > 1

**Correct answer:**

|n^{2} - 1| > 1

### Example Question #31 : Inequalities

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

**Possible Answers:**

-2

-1

-3

-4

All of the answers choices are valid.

**Correct answer:**

-1

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

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

Solve for *x*

**Possible Answers:**

**Correct answer:**

### Example Question #32 : Inequalities

We have , find the solution set for this inequality.

**Possible Answers:**

**Correct answer:**

### Example Question #33 : Inequalities

Fill in the circle with either , , or symbols:

for .

**Possible Answers:**

The rational expression is undefined.

None of the other answers are correct.

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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

Give the solution set of the inequality:

**Possible Answers:**

None of the other responses gives the correct answer.

**Correct answer:**

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:

**Possible Answers:**

None of the other responses gives the correct answer.

**Correct answer:**

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 ?

**Possible Answers:**

**Correct answer:**

In order for a negative multiple to be greater than a number and a positive multiple to be less than that number, that number must be negative itself. -4 is the only negative number available, and thus the correct answer.

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