For what x is 1 x + 3 > 2 x - 3 ?

nidantasnu

nidantasnu

Answered

2022-07-10

For what x is 1 x + 3 > 2 x - 3 ?

Answer & Explanation

Jayvion Tyler

Jayvion Tyler

Expert

2022-07-11Added 23 answers

Step 1
Note that x = - 3 and x = 3 are not solutions since one or the other side of the inequality is undefined for these values of x.
Split the remaining possibilities into cases:
Case x ( - , - 3 ) ( 3 , )
x + 3 and x - 3 are both negative or both positive.
In either case ( x + 3 ) ( x - 3 ) > 0 so multiply both sides of the inequality by that to get:
x - 3 > 2 x + 6
Subtract x + 6 from both sides to get:
- 9 > x
Combining with the conditions of the case, that gives us the solution:
x ( - , - 9 )
Case x ( - 3 , 3 ) .
x + 3 > 0 and x - 3 < 0 , so ( x + 3 ) ( x - 3 ) < 0 , so multiply both sides of the inequality by this and reverse the inequality to get:
x - 3 < 2 x + 6
Step 2
Subtract x + 6 from both sides to get:
- 9 < x
Combining with the conditions of the case, that gives us the solution:
x ( - 3 , 3 )
Conclusion
Putting the two cases together, the original inequality holds for all
x ( - , - 9 ) ( - 3 , 3 )

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