Keesha is having trouble solving the following compound inequality. She arrived at a final answer (below) but when she checked her work she discovered that it is incorrect! Find Keesha’s error and explain to her how to fix it and solve the problem correctly. Then, provide the correct answer.
14 < 2x + 12 ≤ 24
-14 – 12 < 2x + 12 – 12 ≤ 24
2 < 2x ≤ 24
2/2 < 2x/2 ≤ 24/2
1 < x ≤ 12
Please help!
Can someone please help?
2 is greater than 1 and less than 12.
11 is greater 1 and less than 12.
12 is greater than 1 and = 12.
14 < 2x + 12 ≤ 24
-14 – 12 < 2x + 12 – 12 ≤ 24
2 < 2x ≤ 24
2/2 < 2x/2 ≤ 24/2
1 < x ≤ 12
is Keesha's answer, which I'm trying to find the error in and solve it correctly but I don't understand, so if someone could please explain how to find the answer it would be greatly appreciated.
Keesha's error occurs when she divides the inequality by 2. She incorrectly writes 2/2 < 2x/2 ≤ 24/2 as 1 < x ≤ 12.
To fix this, let's go through the steps again, but applying the correct operations:
Starting with 14 < 2x + 12 ≤ 24, we subtract 12 from all parts of the inequality:
14 - 12 < 2x + 12 - 12 ≤ 24 - 12
2 < 2x ≤ 12
Next, we divide all parts of the inequality by 2:
2/2 < 2x/2 ≤ 12/2
1 < x ≤ 6
Therefore, the correct answer is 1 < x ≤ 6.
14 < 2x+12 <= 24
14-12 < 2x <= 24
2 < 2x <= 24
1 < x <= 12.
My answer is the same as yours.
All values of x from 2 to 12 satisfies the inequality.