Question
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( s = -0.75 \)
Solution
Solve the equation \( \frac{2}{3}(9-6s)=4(s+3) \).
Solve the equation by following steps:
- step0: Solve for \(s\):
\(\frac{2}{3}\left(9-6s\right)=4\left(s+3\right)\)
- step1: Multiply the terms:
\(6-4s=4\left(s+3\right)\)
- step2: Expand the expression:
\(6-4s=4s+12\)
- step3: Move the expression to the left side:
\(-4s-4s=12-6\)
- step4: Add and subtract:
\(-8s=12-6\)
- step5: Add and subtract:
\(-8s=6\)
- step6: Change the signs:
\(8s=-6\)
- step7: Divide both sides:
\(\frac{8s}{8}=\frac{-6}{8}\)
- step8: Divide the numbers:
\(s=-\frac{3}{4}\)
The solution to the equation \( \frac{2}{3}(9-6s)=4(s+3) \) is \( s = -\frac{3}{4} \) or \( s = -0.75 \).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Extra Insights
To solve the equation \( \frac{2}{3}(9-6 s)=4(s+3) \), first, let's distribute both sides. Starting with the left side: \[ \frac{2}{3} \times 9 - \frac{2}{3} \times 6s = 6 - 4s. \] Now we need to simplify the right side: \[ 4(s + 3) = 4s + 12. \] Now we set both sides of the equation equal: \[ 6 - 4s = 4s + 12. \] Next, let's combine like terms. Add \( 4s \) to both sides: \[ 6 = 8s + 12. \] Now, subtract 12 from both sides: \[ 6 - 12 = 8s, \] \[ -6 = 8s. \] Finally, divide both sides by 8: \[ s = -\frac{6}{8} = -\frac{3}{4}. \] So the solution to the equation is \( s = -\frac{3}{4} \).
