How do you solve -9 < 4x + 3 < 11?

1 Answer
Aug 29, 2015

Answer:

#-3 < x < 2#

Explanation:

Given
#color(white)("XXXX")-9 < 4x + 3 < 11#

Things you can do with expressions in an inequality which maintain the inequality:

  • Add the same amount to each expression
  • Subtract the same amount from each expression
  • Divide each expression by the same amount provided the amount is greater than zero
  • Multiply each expression by the same amount provided the amount is greater than zero

So, we can subtract #3# from each expression, to get:
#color(white)("XXXX")-12 < 4x < 8#

Then we can divide each expression by #4#, to get:
#color(white)("XXXX")-3 < x < 2#