Question

How do you solve and graph `9 ( x - 11 ) > 17 + 7x`?

Answer 1

`color(red)(x>58)`

Explanation:

`9(x−11)>17+7x`

`9x-99 >17+7x`

`9x-7x>17+99`

`2x>116`

`x>58`

Now, plot each graph separately and then shade the area that satisfies the inequality.

Your inequality is `9(x−11)>17+7x`

Your graph is

The blue area represents the region in which `9(x−11)>17+7x`

Check: Test a point in the coloured region.

Try (`150,1200`).

`9(x−11)>17+7x`
`9(150-11)>17+7(150)`
`9×139>17+1050`
`1251>1067`
∴ TRUE