What value of x is in the solution set of 9(2x + 1) < 9x – 18

The answer is:  " x < -3 " .

Explanation:

Given:

  " 9(2x + 1) < 9x – 18 " ;

First , factor out a "9" in the expression on the right-hand side of the inequality:

9x – 18 = 9(x – 2) ;

and rewrite the inequality:

9(2x + 1) < 9(x – 2) ;

Now, divide EACH SIDE of the inequality by "9" ;

[9(2x + 1)] / 9 < [9(x – 2)] / 9 ;

to get:

2x + 1 < x – 2 ; 

Now, subtract "x" and add "2" to each side of the inequality:

2x + 1 – x + 2  <  x – 2  – x + 2 ;

to get:

x + 3 < 0 ;

Subtract "3" from EACH SIDE ;

x + 3 – 3 < 0 – 3 ;

to get:

      " x < -3 "  .

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