Question

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

Answer 1

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

Explanation:

`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

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

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

Explanation:

Given:

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

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

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:

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)`