Question
Solve the inequality: \( 9-2(6 x+1)<-23 \) \( \begin{array}{l}x>\frac{5}{2} \\ x>\frac{39}{12} \\ x<-\frac{5}{2} \\ x<\frac{39}{12}\end{array} \)
Ask by Potter Boone. in Japan
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x > \frac{5}{2} \)
Solution
To solve the inequality:
\[
9 - 2(6x + 1) < -23
\]
**Step 1: Distribute the -2**
\[
9 - 12x - 2 < -23
\]
**Step 2: Combine like terms**
\[
7 - 12x < -23
\]
**Step 3: Isolate the term with \(x\)**
Subtract 7 from both sides:
\[
-12x < -30
\]
**Step 4: Solve for \(x\)**
Divide both sides by -12. **Remember** that dividing by a negative number reverses the inequality sign:
\[
x > \frac{30}{12}
\]
Simplify the fraction:
\[
x > \frac{5}{2}
\]
**Final Answer:**
\[
\boxed{x > \dfrac{5}{2}}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To solve the inequality \( 9-2(6x+1)<-23 \), first distribute the \(-2\): \[ 9 - 12x - 2 < -23 \] Next, combine like terms: \[ 7 - 12x < -23 \] Now, isolate the term with \(x\) by subtracting 7 from both sides: \[ -12x < -30 \] Finally, divide both sides by \(-12\) (remember to flip the inequality sign): \[ x > \frac{30}{12} \] This simplifies to: \[ x > \frac{5}{2} \] So the solution is \( x > \frac{5}{2} \).
