Question

Identify the mistake and correct it in the work shown for solving the following inequality. 9x + 9 > 12x + 6 -3x > -3 x > 1

Answer 1

Given:

The inequality is

`9x+9>12x+6`

To find:

The mistake in the given solution and correct it.

Solution:

We have,

`9x+9>12x+6`

Isolating variable on one side, we get

`9x-12x>6-9`

`-3x>-3`

On dividing both sides by -3, we get

`(-3x)/(-3)<(-3)/(-3)`

Because if an inequality is multiplied or divided by a negative number, then the sign of inequality must be changed.

`x<1`

Therefore, there is a mistake in last step because the sign of inequality remains same after diving it by -3 and the correct solution is
`x<1`.