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
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.
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
14 + -12 < 2x +12 + -12 <_ 24 + -12
2 < 2x <_ 12
2/2 < 2x/2 <_ 12/2
1 < x <_ 6
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.