How do you solve and graph # 3-2k > -4#?

1 Answer
Alan P.
Sep 6, 2015

#k < 7/2#
graph{3-2x < -4 [-2.8, 8.297, -2.854, 2.694]}

Explanation:

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

Things you can do with expressions in an inequality which reverse the direction of the inequality sign:

  • Exchange the expressions with one another on opposite sides of the inequality (when dealing with a single inequality relation)
  • Multiply both sides of the inequality by an amount less than zero
  • Divide both sides of the inequality by an amount less than zero

#3-2k < -4#

Given the above rules, we can subtract #3# from each expression, to get:
#color(white)("XXXX")-2k < -7#

Then we can divide each expression by #-2#, to get:
#color(white)("XXXX")k > 7/2 color(white)("XXXX")#(remember dividing by a value less than zero reverses the inequality sign)

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