Question

Solve this inequality for x.

Answer 1

`\boxed{A}`

Solution Steps:

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1.) Multiply both sides of the equation by 5:

• 
  `81` ×
  `5=405`

• 
  `55` ×
  `5=275`

- Since 5 is positive, the inequality direction remains the same.

Inequality at the end of Step 1:

• 
  `405-(1` ×
  `5+1)` ≤
  `275`

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:

• 
  `405-6x` ≤
  `275`

3.) Subtract 405 from both sides:

• 
  `405-405=` Cancels Out

• 
  `275-405=-130`

- We do this to get 1 number/variable on each side.

Inequality at the end of Step 3:

• 
  `-6x` ≤
  `-130`

4.) Divide both sides by −6:

• 
  `-6x` ÷
  `-6=x`

• 
  `-130` ÷
  `-6=(-130)/(-6)`

- Since −6 is negative, the inequality direction is changed.

Inequality at the end of Step 3:

• 
  `x` ≥
  `(-130)/(-6)`

5.) Reduce the fraction
`\bold{(-130)/(-6)}` to lowest terms by extracting and canceling out −2:

• 
  `-130` ÷
  `-2=65`

• 
  `-6` ÷
  `3`

- Extracting and cancelling out just means dividing. So we just divide the numerator and denominator by -2.

Inequality at the end of Step 5:

• 
  `x` ≥
  `(65)/(3)`

6.) Turn the fraction into a mixed number:

• 
  `(65)/(3)=21(2)/(3)`

- 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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