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Solve this inequality for x.

Solve This Inequality For X class=

Sagot :

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.
  • Add 5 and 1 to get 6.

 - 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
  • [tex]275-405=-130[/tex]

 - 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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