Solve the inequality. If there is no solution, write no solution (still show work).
|2x-7|>1
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.
To solve the inequality |2x-7| > 1, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.
Case 1: 2x - 7 > 1
Adding 7 to both sides, we get:
2x > 8
Dividing both sides by 2, we obtain:
x > 4
Case 2: 2x - 7 < -1
Adding 7 to both sides, we get:
2x < 6
Dividing both sides by 2, we obtain:
x < 3
Therefore, the solution to the inequality |2x-7| > 1 is x < 3 or x > 4.
To solve the inequality |2x-7| > 1, we need to consider two cases: when 2x-7 is positive and when 2x-7 is negative.
Case 1: 2x-7 is positive
If 2x-7 is positive, then the absolute value of 2x-7 is equal to 2x-7. Therefore, we can rewrite the inequality as 2x-7 > 1.
Solving this inequality, we add 7 to both sides:
2x - 7 + 7 > 1 + 7
2x > 8
Next, we divide both sides by 2 to solve for x:
(2x)/2 > 8/2
x > 4
Case 2: 2x-7 is negative
If 2x-7 is negative, then the absolute value of 2x-7 is equal to -(2x-7). Therefore, we can rewrite the inequality as -(2x-7) > 1.
To solve this, we multiply both sides by -1, which reverses the inequality sign:
-(-(2x-7)) < -1(-1)
2x-7 < -1
Next, we add 7 to both sides:
2x - 7 + 7 < -1 + 7
2x < 6
Finally, dividing both sides by 2 to solve for x:
(2x)/2 < 6/2
x < 3
Combining the results from both cases, we have two inequalities: x > 4 and x < 3.
However, this creates a contradiction since there is no value of x that simultaneously satisfies x > 4 and x < 3. Therefore, there is no solution to the inequality |2x-7| > 1.