GRE Math : How to add negative numbers

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Example Question #1 : How To Add Negative Numbers

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

Possible Answers:

$4x^{4}+2x+5$ $\displaystyle 4x^{4}+2x+5$

$2x^{4}+2x+9$ $\displaystyle 2x^{4}+2x+9$

$2x^{4}+5$ $\displaystyle 2x^{4}+5$

$2x^{4}+2x+5$ $\displaystyle 2x^{4}+2x+5$

$2x^{4}+9$ $\displaystyle 2x^{4}+9$

Correct answer:

$2x^{4}+9$ $\displaystyle 2x^{4}+9$

Explanation:

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

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

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

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

$2x^{4}+9$ $\displaystyle 2x^{4}+9$

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Example Question #2 : How To Add Negative Numbers

Solve for $\displaystyle x$ :

$\displaystyle 2x + 47 = -47$

Possible Answers:

x = 47 $\displaystyle x = 47$

x = -57 $\displaystyle x = -57$

x = -37 $\displaystyle x = -37$

x = -47 $\displaystyle x = -47$

x = -94 $\displaystyle x = -94$

Correct answer:

x = -47 $\displaystyle x = -47$

Explanation:

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

$\displaystyle 2x + 47 = -47$

$\displaystyle 2x + 47 + (- 47) = -47 + (-47)$

Taking this step will elminate the $\displaystyle 47$ on the side with $\displaystyle x$ :

$\displaystyle 2x = -94$

Now divide by $\displaystyle 2$ to solve for $\displaystyle x$ :

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

x = -47 $\displaystyle x = -47$

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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Example Question #133 : Arithmetic

Solve for $\displaystyle x$ :

$\displaystyle 2x + 52 = -30$

Possible Answers:

x = 41 $\displaystyle x = 41$

x = -41 $\displaystyle x = -41$

x = -31 $\displaystyle x = -31$

x = 31 $\displaystyle x = 31$

x = 51 $\displaystyle x = 51$

Correct answer:

x = -41 $\displaystyle x = -41$

Explanation:

To solve this problem, first you must add $\displaystyle -52$ to both sides of the problem. This will yield a result on the right side of the equation of $\displaystyle -82$ , 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 x = -41 $\displaystyle x = -41$ .

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GRE Math : How to add negative numbers

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1 : How To Add Negative Numbers

Example Question #2 : How To Add Negative Numbers

Example Question #133 : Arithmetic

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