How do you solve the inequality #6 <x - 6 <=8#?

Answer 1

#12 < x < 14#

When we talk about inequalities, its necessary for us to split it in two parts: #? < x# and #x < ?#. In this case, we first have #6 < x -6# that becomes #12 < x# by passing the #-6# to the other side of the inequality. Then, we solve the second part: #x - 6 < 8# that becomes # x < 14# by passing the #-6# to the other side of the inequality. Now, we just need to join both parts, creating #12< x < 14#.

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Answer 2

Abigail Allen

To solve the inequality (6 < x - 6 \leq 8), first, add (6) to all parts of the inequality. This gives (12 < x \leq 14). So, the solution is (12 < x \leq 14).

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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 the inequality #6 &lt;x - 6 &lt;=8#?

How do you solve the inequality #6 <x - 6 <=8#?