How do you solve the inequality #8 − 2x < 4#?

1 Answer
Sep 8, 2015

Answer:

#x > 2#

Explanation:

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

  • 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

Things you can do with expressions in an inequality which reverse the inequality orientation.

  • Divide each expression by the same amount when the amount is less than zero
  • Multiply each expression by the same amount when the amount is less than zero

Given the above rules:

#color(white)("XXXX")8-2x < 4#
subtract #8# from both sides:
#color(white)("XXXX")-2x < -4#
divide both sides by #(-2)#, which reverses orientation of inequality
#color(white)("XXXX")x > 2#