How do you solve 1<3x+4<10?

Answer 1

#-1 < x < 2#

Adding or Subtracting a constant from each component of an inequality and Multiplying or Dividing by a constant greater than #0#, does not effect the orientation of the inequality.

So #color(white)("XXXX")##1 < 3x +4 <10# becomes by subtracting #4# from each component #color(white)("XXXX")##-3 < 3x < 6# which becomes by dividing each component by #3# #color(white)("XXXX")##-1 < x < 2#

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Answer 2

Eva Abramson

To solve the inequality (1 < 3x + 4 < 10), we need to isolate (x).

First, subtract 4 from all parts of the inequality:

[ 1 - 4 < 3x + 4 - 4 < 10 - 4 ] [ -3 < 3x < 6 ]

Next, divide by 3:

[ \frac{-3}{3} < \frac{3x}{3} < \frac{6}{3} ] [ -1 < x < 2 ]

So the solution to the inequality (1 < 3x + 4 < 10) is (-1 < x < 2).

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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 1&lt;3x+4&lt;10?

How do you solve 1<3x+4<10?