Solution To Inequality 1
#-4x < -16#
We will divide each side of the inequality by #color(blue)(-4)# to solve for #x# while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:
#(-4x)/color(blue)(-4) color(red)(>) (-16)/color(blue)(-4)#
#(color(blue)(cancel(color(black)(-4)))x)/cancel(color(blue)(-4)) color(red)(>) 4#
#x > 4#
Solution To Inequality 2
#x + 4 > 5#
We will subtract #color(red)(4)# from each side of the equation to solve for #x# while keeping the equation balanced:
#x + 4 - color(red)(4) > 5 - color(red)(4)#
#x + 0 > 1#
#x > 1#
The Solutions Are: #x > 1# and #x > 4#
However, because the interval #(1, 4)# is a valid solution for Inequality 2 but not for inequality 1 the solution is:
#x > 4#
Interval notation:
#(4, +oo)#
