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How do you solve #5<2x+7<13#?

Answer 1

See full solution process below

While solving this set of inequalities we need to perform each operation to all three parts of the set of inequalities to keep everything balanced.

First, subtract #color(red)(7) from each term in the inequalities:

#5 - color(red)(7) < 2x + 7 - color(red)(7) < 13 - color(red)(7)#

#-2 < 2x + 0 < 6#

#-2 < 2x < 6#

Now, we can divide each portion of the inequalities by #color(red)(2)# to solve for #x# while keeping the inequality set balanced:

#(-2)/color(red)(2) < (2x)/color(red)(2) < 6/color(red)(2)#

#-1 < (color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) < 3#

#-1 < x < 3#

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Answer 2

Eli Assouline

To solve the compound inequality (5 < 2x + 7 < 13), follow these steps:

Subtract 7 from all parts of the inequality: (5 - 7 < 2x < 13 - 7) (-2 < 2x < 6)
Divide all parts by 2: (-1 < x < 3)

So, the solution to the compound inequality is (-1 < x < 3).

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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.

How do you solve #5&lt;2x+7&lt;13#?

How do you solve #5<2x+7<13#?