GRE Math : How to find the solution to an inequality with subtraction

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Example Question #3 : Inequalities

The cost, in cents, of manufacturing $\dpi{100} \small x$ pencils is $\dpi{100} \small 1200+20x$ , where 1200 is the number of cents required to run the factory regardless of the number of pencils made, and 20 represents the per-unit cost, in cents, of making each pencil. The pencils sell for 50 cents each. What number of pencils would need to be sold so that the revenue received is at least equal to the manufacturing cost?

Possible Answers:

$\dpi{100} \small 30$

$\dpi{100} \small 27$

$\dpi{100} \small 36$

$\dpi{100} \small 33$

$\dpi{100} \small 40$

Correct answer:

$\dpi{100} \small 40$

Explanation:

If each pencil sells at 50 cents, $\dpi{100} \small x$ pencils will sell at $\dpi{100} \small 50x$ . The smallest value of $\dpi{100} \small x$ such that

$\dpi{100} \small 50x\geq 1200+20x$

$\dpi{100} \small x\geq 40$

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

Find the slope of the inequality equation $y-7< x+2y-14$

Possible Answers:

–1

–7

Correct answer:

–1

Explanation:

The answer is:

$y-7< x+2y-14$

$-y-7< x-14$

$-1(-y< x-7)$

$y > -x+7$

From the equation we can see that the slope is –1.

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

and are both integers.

If y-3x>21 , y>1 , and y<4 , which of the following is a possible value of ?

Possible Answers:

Correct answer:

Explanation:

Take the values of y that are possible, i.e. 2 and 3, and plug them into the first inequality. First, plug in 2. 2 – 3x > 21. Subtract 2 from both sides, and then divide by –3. Don't forget that when you divide or multiply by a negative number in an inequality you must flip the inequality sign. Thus, x < –19/3. Now plug in 3. We find, following the same steps, that when y=3, x < –6. Thus –7 is the correct answer.

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

Quantity A:

The value(s) for which the following function is undefined:

$f(x)=\sqrt{5x-135}$

Quantity B:

Which of the following is true?

Possible Answers:

A comparison cannot be detemined from the given information.

Quantity A is larger.

Quantity B is larger.

The two quantities are equal.

Correct answer:

Quantity B is larger.

Explanation:

This question is not as hard as it seems. Remember that for real numbers, square roots cannot be taken of negative numbers. Therefore, we know that this function is undefined for:

5x-135 < 0

This is simple to solve. Merely add 135 to both sides:

5x<135

Then, divide by :

x < 27

Therefore, quantity A is less than quantity B. This means that quantity B is greater than it.

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

|x+12|<42

Quantity A:

Quantity B:

Which of the following is true?

Possible Answers:

Quantity B is larger.

Quantity A is larger.

A comparison cannot be detemined from the given information.

The two quantities are equal.

Correct answer:

A comparison cannot be detemined from the given information.

Explanation:

Recall that when you have an absolute value and an inequality like

|x+12|<42 ,

this is the same as saying that x+12 must be between and . You can rewrite it:

-42 < x+12<42

To solve this, you merely need to subtract from all three values:

-54 < x <30

Since is between and , it could be both larger or smaller than . Therefore, you cannot determine the relationship based on the given information.

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GRE Math : How to find the solution to an inequality with subtraction

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #3 : Inequalities

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

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

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

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

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