Question
Solve the inequality. If there is no solution, write no solution (still show work).
|2x-7|>1
|2x-7|>1
Answers
GPT 3.5
To solve the inequality |2x-7|>1, we can split it into two separate inequalities:
1) 2x-7>1
2) 2x-7<-1
For 1), we add 7 to both sides:
2x-7+7 > 1+7
2x > 8
Finally, we divide both sides by 2:
x > 4
For 2), we add 7 to both sides:
2x-7+7 < -1+7
2x < 6
Finally, we divide both sides by 2:
x < 3
Thus, the solution to the inequality |2x-7|>1 is x < 3 or x > 4.
1) 2x-7>1
2) 2x-7<-1
For 1), we add 7 to both sides:
2x-7+7 > 1+7
2x > 8
Finally, we divide both sides by 2:
x > 4
For 2), we add 7 to both sides:
2x-7+7 < -1+7
2x < 6
Finally, we divide both sides by 2:
x < 3
Thus, the solution to the inequality |2x-7|>1 is x < 3 or x > 4.