How do you solve and write the following in interval notation: #-4x< -16# and #x+ 4 > 5#?

1 Answer
Jul 21, 2017

Answer:

See a solution process below:

Explanation:

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)#