Negative Numbers - GRE Quantitative Reasoning

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Question

Simplify $(7+x+3x^{4})-(x^{4}+x-2)$

Answer

The answer is $2x^{4}+9$

Make sure to distribute negatives throughout the second half of the equation.

$(7+x+3x^{4})-(x^{4}+x-2)$

$(3x^{4}+x+7)+(-x^{4}-x+2)$

$2x^{4}+9$

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Question

Solve for :

Answer

To solve this problem, you need to get your variable isolated on one side of the equation:

Taking this step will elminate the on the side with :

Now divide by to solve for :

$x = -\frac{94}{2}$

The important step here is to be able to add the negative numbers. When you add negative numbers, they create lower negative numbers (if you prefer to think about it another way, you can think of adding negative numbers as subtracting one of the negative numbers from the other).

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Question

Solve for :

Answer

To solve this problem, first you must add to both sides of the problem. This will yield a result on the right side of the equation of , because a negative number added to a negative number will create a lower number (i.e. further away from zero, and still negative). Then you divide both sides by two, and you are left with .

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Question

Simplify $(7+x+3x^{4})-(x^{4}+x-2)$

Answer

The answer is $2x^{4}+9$

Make sure to distribute negatives throughout the second half of the equation.

$(7+x+3x^{4})-(x^{4}+x-2)$

$(3x^{4}+x+7)+(-x^{4}-x+2)$

$2x^{4}+9$

Compare your answer with the correct one above

Question

Solve for :

Answer

To solve this problem, you need to get your variable isolated on one side of the equation:

Taking this step will elminate the on the side with :

Now divide by to solve for :

$x = -\frac{94}{2}$

The important step here is to be able to add the negative numbers. When you add negative numbers, they create lower negative numbers (if you prefer to think about it another way, you can think of adding negative numbers as subtracting one of the negative numbers from the other).

Compare your answer with the correct one above

Question

Solve for :

Answer

To solve this problem, first you must add to both sides of the problem. This will yield a result on the right side of the equation of , because a negative number added to a negative number will create a lower number (i.e. further away from zero, and still negative). Then you divide both sides by two, and you are left with .

Compare your answer with the correct one above

Question

Simplify $(7+x+3x^{4})-(x^{4}+x-2)$

Answer

The answer is $2x^{4}+9$

Make sure to distribute negatives throughout the second half of the equation.

$(7+x+3x^{4})-(x^{4}+x-2)$

$(3x^{4}+x+7)+(-x^{4}-x+2)$

$2x^{4}+9$

Compare your answer with the correct one above

Question

Solve for :

Answer

To solve this problem, you need to get your variable isolated on one side of the equation:

Taking this step will elminate the on the side with :

Now divide by to solve for :

$x = -\frac{94}{2}$

The important step here is to be able to add the negative numbers. When you add negative numbers, they create lower negative numbers (if you prefer to think about it another way, you can think of adding negative numbers as subtracting one of the negative numbers from the other).

Compare your answer with the correct one above

Question

Solve for :

Answer

To solve this problem, first you must add to both sides of the problem. This will yield a result on the right side of the equation of , because a negative number added to a negative number will create a lower number (i.e. further away from zero, and still negative). Then you divide both sides by two, and you are left with .

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Question

Find the value of .

$-2x= -\frac{1}{3}$

Answer

To solve for , divide each side of the equation by -2.

$\left(-\frac{1}{3}\right) \div-2$ is the same as

$-\frac{1}{3} \cdot -\frac{1}{2}$ which is POSITIVE $\frac{1}{6}$

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Question

What is $\frac{-36}{-9}$ ?

Answer

A negative number divided by a negative number always results in a positive number. divided by equals . Since the answer is positive, the answer cannot be or any other negative number.

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Question

Solve for :

Answer

Begin by isolating your variable.

Subtract from both sides:

, or

Next, subtract from both sides:

, or

Then, divide both sides by :

$x=\frac{-10}{-5}$

Recall that division of a negative by a negative gives you a positive, therefore:

$x=\frac{10}{5}$ or

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Question

Solve for :

Answer

To solve this equation, you need to isolate the variable on one side. We can accomplish this by dividing by on both sides:

$y = \frac{-45}{-3}$

Anytime you divide, if the signs are the same (i.e. two positive, or two negative), you'll get a positive result. If the signs are opposites (i.e. one positive, one negative) then you get a negative.

Both of the numbers here are negative, so we will have a positive result:

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Question

Solve for :

Answer

To solve, you need to isolate the variable. We first subtract then divide by :

$p = \frac{-6}{2}$

When dividing, if the signs of the numbers are the same (i.e. both positive, or both negative), you yield a positive result. If the signs of the numbers are opposites (i.e. one of each), then you yield a negative result.

Therefore:

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Question

Find the value of .

$-2x= -\frac{1}{3}$

Answer

To solve for , divide each side of the equation by -2.

$\left(-\frac{1}{3}\right) \div-2$ is the same as

$-\frac{1}{3} \cdot -\frac{1}{2}$ which is POSITIVE $\frac{1}{6}$

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Question

What is $\frac{-36}{-9}$ ?

Answer

A negative number divided by a negative number always results in a positive number. divided by equals . Since the answer is positive, the answer cannot be or any other negative number.

Compare your answer with the correct one above

Question

Solve for :

Answer

Begin by isolating your variable.

Subtract from both sides:

, or

Next, subtract from both sides:

, or

Then, divide both sides by :

$x=\frac{-10}{-5}$

Recall that division of a negative by a negative gives you a positive, therefore:

$x=\frac{10}{5}$ or

Compare your answer with the correct one above

Question

Solve for :

Answer

To solve this equation, you need to isolate the variable on one side. We can accomplish this by dividing by on both sides:

$y = \frac{-45}{-3}$

Anytime you divide, if the signs are the same (i.e. two positive, or two negative), you'll get a positive result. If the signs are opposites (i.e. one positive, one negative) then you get a negative.

Both of the numbers here are negative, so we will have a positive result:

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Question

Solve for :

Answer

To solve, you need to isolate the variable. We first subtract then divide by :

$p = \frac{-6}{2}$

When dividing, if the signs of the numbers are the same (i.e. both positive, or both negative), you yield a positive result. If the signs of the numbers are opposites (i.e. one of each), then you yield a negative result.

Therefore:

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Question

Find the value of .

$-2x= -\frac{1}{3}$

Answer

To solve for , divide each side of the equation by -2.

$\left(-\frac{1}{3}\right) \div-2$ is the same as

$-\frac{1}{3} \cdot -\frac{1}{2}$ which is POSITIVE $\frac{1}{6}$

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