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sveta [45]
3 years ago
12

Solve and graph the absolute value inequality: |2x + 4| > 14.

Mathematics
1 answer:
Aloiza [94]3 years ago
4 0

Answer:

"number line with open circles on negative 9 and 5, shading going in the opposite directions."

Step-by-step explanation:

Your inequality doesn't include an equal sign so there will be no closed holes. It will only be open holes.

|u|>14 means that the number u has to be greater than 14 or less than -14.  These numbers I describe just now all have a distance greater than 14 from 0.

So |u|>14 implies u>14 or u<-14.

But we are solving |2x+4|>14 so this implies we have 2x+4>14 or 2x+4<-14.

2x+4>14

Subtract 4 on both sides:

2x    >10

Divide both sides by 2:

x      >5

2x+4<-14

Subtract 4 on both sides:

2x    <-18

Divide both sides by 2:

x      <-9

So our solution is x>5 or x<-9.

Graphing!

~~~~~~~O                                         O~~~~~~~~

-----------(-9)---------------------------------(5)---------------

So we shaded to the right of 5 because our inequality says x is bigger than 5.

We shaded to the left of -9 because our inequality says x is less than -9.

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Two-thirds a number plus 4 is 7
ICE Princess25 [194]

The equation (form) is: \frac{2}{3}x + 4 = 7

The solution of the equation is: x = \frac{9}{2}


Explanation:

First, let's call the number we are going to solve for "x".

Then two thirds of this number can be written as:

\frac{2}{3}x

Then "plus 4" means add 4 we get:

\frac{2}{3}x + 4

"is 7" means that the above expression is equal to 7 (as follows):

\frac{2}{3}x + 4 = 7

The solution of the above equation is:

\frac{2}{3}x + 4 = 7 \\ \frac{2}{3}x = 3 \\ x =  \frac{9}{2}

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which expression is equivalent to (^3sqrtm)^7 in exponential form? a) 7 m/3 b) 3 m/7 c) m 3/7 d) m 7/3
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A student had taken 7 tests and received scores of 88, 73, 81, 83, 79, 73, and 97.
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Answer:

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