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

$\dfrac{-3x}{-3}<\dfrac{-3}{-3}$

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 $x<1$.