Question

The inequality 6 - 2/3x < x - 9 is equivalent to

Answer 1

For this case we have the following inequality:

`6- \frac {2} {3} x <x-9`

We add
`\frac {2} {3} x` to both sides of the inequality:

`6 <\frac {2} {3} x + x-9\\6 <\frac {2 * 1 + 3 * 1} {3} x-9\\6 <\frac {2 + 3} {3} x-9\\6 <\frac {5} {3} x-9\\`

We add 9 to both sides of the inequality:

`6 + 9 <\frac {5} {3} x\\15 <\frac {5} {3} x`

We multiply by 3 on both sides of the inequality:

`15 * 3 <5x\\45 <5x`

We divide between 5 on both sides of the inequality:

`\frac {45} {5} <x\\9 <x`

Thus, the solution is given by all values of x greater than 9.

Answer:

`x> 9` is equivalent to the given inequality.