- Submitted By: Slim-Fahrenheit
- Date Submitted: 08/25/2016 9:11 PM
- Category: Science
- Words: 3496
- Page: 14

GMAT Maths free flashcards

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o Step 3: set the predominant sign for each

term under each condition, and solve the

equation. In the example.

Absolute value

• Formulas to remember:

o

o

o

o By definition of |x|, |x| = x if x ≥ 0 and |x|

= -x if x < 0

• Absolute value exercises like: How many

solutions will this equation have? |x+3| – |4-x|

= |8+x| ---> we apply the "Critical Values"

method for absolute values equations:

o Step 1: do each absolute term equal to zero

to obtain critical values. In the example,

critical values are -3, 4, -8.

o Step 2: place them in the Real numbers line

to make all the possible intervals. Note that

you have to include critical values in the

intervals, that is why we put the term "less

or equal" and "big or equal"... we put them

as below by convention. In the example, the

intervals (or conditions) are:

Condition 1: -(x+3) - (4-x) = -(8+x) --> x = -1

Condition 2: -(x+3) - (4-x) = (8+x) --> x = -15

Condition 3: (x+3) - (4-x) = (8+x) --> x = 9

Condition 4: (x+3) + (4-x) = (8+x) --> x = -1

o Step 4: check if the solution satisfies the

initial condition. In the example:

Condition 1: NO, -1 is not less than -8

Condition 2: NO, -15 is not between -8 and -3

(including -8 in the interval and not -3)

Condition 3: NO, 9 is not between -3 and 4

(including -3 in the interval and not 4)

Condition 4: NO, -1 is...