Question

Please help!!

Solve the inequality for x. Show each step of the solution. 12 > 9(2 − 3)− 21

Answer 1

True

Explanation:

12 > 9(2-3) - 21

First thing you do is use the distributive property.

9 times 2 is 18.

9 times -3 is -27

12 > 18 - 27 - 21

The second thing that you do is subtract everything on the other side of the less than sign.

18 - 27 = -9

-9 - 21 = -30

12 is greater than -30 because a positive number is always greater than a negative number.

Answer 2

Answer: The required solution for x is
`x<3.33.`

Step-by-step explanation: We are given to solve the following inequality for x :

`12>9(2x-3)-21~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

To solve the given inequality for x, we must bring x on the left hand side and other terms on the right hand side of the inequality.

From inequality (i), we have

`12>9(2x-3)-21\\\\\Rightarrow 12>18x-27-21\\\\\Rightarrow 12>18x-48\\\\\Rightarrow 12+48>18x\\\\\Rightarrow 60>18x\\\\\Rightarrow 18x<60~~~~~~~~~~[\textup{since }a>b~~~\Rightarrow b<a]\\\\\Rightarrow x<(60)/(18)\\\\\Rightarrow x<3.33.`

Thus, the required solution for x is
`x<3.33.`