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

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #1924 : Sat Mathematics

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

Possible Answers:

16n2 - 1 = 0

n2 < n

|n2 - 1| > 1

(n-1)2 > n

n2 < 2n

Correct answer:

|n2 - 1| > 1

Explanation:

N_part_1

N_part_2

N_part_3

N_part_4

N_part_5

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

(√(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

Explanation:

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

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

Solve for x

\small 3x+7 \geq -2x+4

 

Possible Answers:

\small x \geq \frac{3}{5}

\small x \geq -\frac{3}{5}

\small x \leq -\frac{3}{5}

\small x \leq \frac{3}{5}

Correct answer:

\small x \geq -\frac{3}{5}

Explanation:

\small 3x+7 \geq -2x+4

\small 3x \geq -2x-3

\small 5x \geq -3

\small x\geq -\frac{3}{5}

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

We have , find the solution set for this inequality. 

Possible Answers:

Correct answer:

Explanation:

Example Question #6 : How To Find The Solution To An Inequality With Multiplication

Fill in the circle with either <, >, or = symbols:

(x-3)\circ\frac{x^2-9}{x+3} for x\geq 3.

 

Possible Answers:

(x-3)=\frac{x^2-9}{x+3}

(x-3)> \frac{x^2-9}{x+3}

None of the other answers are correct.

(x-3)< \frac{x^2-9}{x+3}

The rational expression is undefined.

Correct answer:

(x-3)=\frac{x^2-9}{x+3}

Explanation:

(x-3)\circ\frac{x^2-9}{x+3}

Let us simplify the second expression. We know that:

(x^2-9)=(x+3)(x-3)

So we can cancel out as follows:

\frac{x^2-9}{x+3}=\frac{(x+3)(x-3)}{(x+3)}=x-3

(x-3)=\frac{x^2-9}{x+3}

 

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:

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?

Possible Answers:

Correct answer:

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 #151 : Algebra

Give the solution set of the inequality:

Possible Answers:

None of the other responses gives the correct answer.

Correct answer:

Explanation:

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

or, in interval form,

.

Example Question #5 : 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:

Explanation:

or, in interval notation, .

Example Question #152 : Algebra

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

Possible Answers:

Correct answer:

Explanation:

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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