How do you solve #\frac { x } { 6} + 8> 27#?

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Answer 1 · 2018-02-09T12:48:58

Solution : # x> 114 or (114,oo)#

#x/6+8 >27 or x/6 >27-8 or x/6 >19or x > 19*6 # or

#x > 114 #.

Solution : # x> 114 or (114,oo)# [Ans]

Answer 2 · 2018-02-09T13:12:16

Required Solution: #color(blue)(x>114#

Using Interval Notation: #color(blue)((114, oo)#

Given:

#color(red)((x/6) + 8 > 27#

Please refer to the image of the graph of the inequality below:

enter image source here

Next, we will simplify the inequality and then draw the graph again.

Then, compare the solutions on the graphs for comprehension.

Subtract #color(blue)8# from both sides.

#rArr (x/6) + 8 -color(blue)(8) > 27 - color(blue)(8) #

#rArr (x/6) + cancel 8 - cancel color(blue)(8) > 27 - color(blue)(8) #

#rArr (x/6) > 19#

Multiply both sides by 6

#(x/6)*6 > 19*6#

#(x/cancel 6)* cancel 6 > 19*6#

Simplify to get:

#x> 114#

Please refer to the image of the graph of the inequality below:

enter image source here

When we compare the two graphs, we observe that they produce identical solutions.

Hence, our final solutions are:

Solution: #color(blue)(x>114#

Using Interval Notation: #color(blue)((114, oo)#