Question
Solve the inequality \( 7(x-2)<-5 \) \( \begin{array}{l}x>9 / 7 \\ x<9 / 7 \\ x<-9 / 7 \\ x>-9 / 7\end{array} \)
Ask by Sherman Barnett. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution is \( x < \frac{9}{7} \).
Solution
We start with the inequality:
7(x – 2) < –5
Step 1: Distribute the 7:
7x – 14 < –5
Step 2: Add 14 to both sides to isolate 7x:
7x < 9
Step 3: Divide both sides by 7:
x < 9/7
Thus, the solution is x < 9/7, which corresponds to the second option in the list.
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Simplify this solution Bonus Knowledge
To solve the inequality \( 7(x-2)<-5 \), we start by isolating \( x \): 1. Divide both sides by 7: \[ x - 2 < -\frac{5}{7} \] 2. Add 2 to both sides: \[ x < -\frac{5}{7} + 2 \] 3. Convert 2 into a fraction with a common denominator: \[ 2 = \frac{14}{7} \] 4. Now perform the addition: \[ x < -\frac{5}{7} + \frac{14}{7} = \frac{9}{7} \] Thus, the solution is: \[ x < \frac{9}{7} \] The answer from the choices provided is \( x < 9 / 7 \).
