Answer:
[tex]\boxed{A}[/tex]
Solution Steps:
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1.) Multiply both sides of the equation by 5:
- [tex]81[/tex] × [tex]5=405[/tex]
- [tex]55[/tex] × [tex]5=275[/tex]
- Since 5 is positive, the inequality direction remains the same.
Inequality at the end of Step 1:
- [tex]405-(1[/tex] × [tex]5+1)[/tex] ≤ [tex]275[/tex]
2.) Solve the parenthesis:
- Multiply 1 and 5 to get 5.
- We turn the fraction into parenthesis by multiplying because a fraction is originally is dividing, so we have to do the opposite, which in this case is multiplying.
Inequality at the end of Step 2:
- [tex]405-6x[/tex] ≤ [tex]275[/tex]
3.) Subtract 405 from both sides:
- [tex]405-405=[/tex] Cancels Out
- We do this to get 1 number/variable on each side.
Inequality at the end of Step 3:
- [tex]-6x[/tex] ≤ [tex]-130[/tex]
4.) Divide both sides by −6:
- [tex]-6x[/tex] ÷ [tex]-6=x[/tex]
- [tex]-130[/tex] ÷ [tex]-6=\frac{-130}{-6}[/tex]
- Since −6 is negative, the inequality direction is changed.
Inequality at the end of Step 3:
- [tex]x[/tex] ≥ [tex]\frac{-130}{-6}[/tex]
5.) Reduce the fraction [tex]\bold{\frac{-130}{-6}}[/tex] to lowest terms by extracting and canceling out −2:
- [tex]-130[/tex] ÷ [tex]-2=65[/tex]
- [tex]-6[/tex] ÷ [tex]3[/tex]
- Extracting and cancelling out just means dividing. So we just divide the numerator and denominator by -2.
Inequality at the end of Step 5:
- [tex]x[/tex] ≥ [tex]\frac{65}{3}[/tex]
6.) Turn the fraction into a mixed number:
- [tex]\frac{65}{3}=21\frac{2}{3}[/tex]
- You can figure this out by dividing 65 by 3 which gives you a decimal, then turn the decimal into a fraction.
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