How do you solve the inequality #-5<=x+8<15#?

Answer 1

See the entire solution process below:

Subtract #color(red)(8)# from each segment of the system of inequalities to solve for #x# while keeping the system balanced:
#-5 - color(red)(8) <= x + 8 - color(red)(8) < 15 - color(red)(8)#
#-13 <= x + 0 < 7#
#-13 <= x < 7#

Or

#x >= -13# and #x < 7#

Or, in interval form:

#(-13, 7]#
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Answer 2

-13#<=#x#<# 7

There are two ways to do this.

The first way is to separate the inequalities and go from there,

Given: -5#<=#x + 8#<# 15
Separated: -5#<=#x + 8 , and x + 8#<#15
Then simply solve for x by subtracting 8: -13#<=#x , and x#<#7
Finally combine to get: -13#<=#x#<# 7

The second method to solve this is to do it together,

Given: -5#<=#x + 8#<# 15
Subtract 8 from both sides and get the answer: -13#<=#x#<# 7
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Answer 3

To solve the inequality ( -5 \leq x + 8 < 15 ), follow these steps:

  1. Subtract 8 from all parts of the inequality: ( -5 - 8 \leq x + 8 - 8 < 15 - 8 ) This simplifies to ( -13 \leq x < 7 ).

  2. Therefore, the solution to the inequality is ( -13 \leq x < 7 ).

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Answer 4

To solve the inequality (-5 \leq x + 8 < 15), first, subtract 8 from all parts of the inequality to isolate (x). This gives (-5 - 8 \leq x < 15 - 8), which simplifies to (-13 \leq x < 7). Therefore, the solution for (x) is all real numbers greater than or equal to (-13) and less than (7), expressed as (-13 \leq x < 7).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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