Question
Solve the inequality for \( w \). \[ 7 w-39>-2(6-8 w) \] Simplify your answer as much as possible.
Ask by Fleming Todd. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution is \( w < -3 \).
Solution
To solve the inequality
7w - 39 > -2(6 - 8w),
first distribute -2 on the right side:
7w - 39 > -12 + 16w.
Next, subtract 7w from both sides to move terms involving w to one side:
-39 > -12 + 9w.
Now, add 12 to both sides to isolate the 9w term:
-27 > 9w.
Finally, divide both sides by 9, remembering that dividing by a positive number does not change the inequality direction:
-3 > w.
This can be rewritten as
w < -3.
Thus, the solution is: w < -3.
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Simplify this solution Extra Insights
To solve the inequality \( 7w - 39 > -2(6 - 8w) \), we first distribute the \(-2\) on the right side: \[ 7w - 39 > -12 + 16w \] Next, we rearrange the inequality to get all terms involving \(w\) on one side and constant terms on the other: \[ 7w - 16w > -12 + 39 \] This simplifies to: \[ -9w > 27 \] Now, we divide both sides by \(-9\). Remember, when dividing by a negative number, we flip the inequality sign: \[ w < -3 \] Thus, the solution to the inequality is: \[ w < -3 \]
