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
Above 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.
where did that -14 in step 2 come from?
And the 12 should have been subtracted from all three quantities.
It should have been
14 - 12 < 2x + 12 - 12 ≤ 24 - 12
2 < 2x ≤ 12
1 < x ≤ 6
Thank you so much!
The RIGHT answer is: -12 should of been added to all three quantities.
14 + -12 < 2x +12 + -12 <_ 24 + -12
2 < 2x <_ 12
2/2 < 2x/2 <_ 12/2
1 < x <_ 6
To solve the compound inequality 14 < 2x + 12 ≤ 24 correctly, let’s go through the steps:
Step 1: Start by solving the left inequality, 14 < 2x + 12. To isolate the variable, we need to subtract 12 from both sides:
14 - 12 < 2x + 12 - 12
2 < 2x
Step 2: Next, solve the right inequality, 2x + 12 ≤ 24. To isolate the variable, we need to subtract 12 from both sides:
2x + 12 - 12 ≤ 24 - 12
2x ≤ 12
Step 3: Now, it’s important to remember that we are looking for values of x that satisfy both inequalities simultaneously. The solution lies in the overlap of both ranges.
Combining the results from steps 1 and 2, we have 2 < 2x ≤ 12.
Step 4: To isolate the x variable, divide both sides of the inequality by 2:
2/2 < 2x/2 ≤ 12/2
1 < x ≤ 6
Therefore, the correct solution to the compound inequality is 1 < x ≤ 6.
Keesha's error was in step 4 where she divided all sides of the inequality by 2, resulting in 1 < x ≤ 12. Instead, she should divide each term separately.
By correctly dividing each term, we obtain 1 < x ≤ 6 as the final solution.