Question

1 fill in the blank 1 point solve the following equation. if there are infinite solutions, type infinite. if there are no \\(5(2 - 11n) + 4n = 51 - 10n\\) \\(n=\\) type your answer... 3 fill in the blank 1 point solve the equation for all values. - type the smaller value first. - if you get a decimal as a solution, type your answer as a simplified, improper fraction - if there is no solution, type no in both boxes. \\(8|-9n - 9| + 8 = 80\\) \\(n=\\) type your answer... and type your answer...

Explanation:

Question 1

Step1: Expand the left side

Using the distributive property \(a(b + c)=ab+ac\), we expand \(5(2 - 11n)\) to get \(10-55n\). So the equation becomes \(10-55n + 4n=51-10n\).

Step2: Combine like terms on the left

Combine \(-55n\) and \(4n\) to get \(-51n\). So the equation is \(10-51n=51-10n\).

Step3: Add \(51n\) to both sides

Adding \(51n\) to both sides gives \(10=51 + 41n\).

Step4: Subtract 51 from both sides

Subtracting 51 from both sides: \(10-51=41n\), which simplifies to \(-41 = 41n\).

Step5: Divide both sides by 41

Dividing both sides by 41: \(n=\frac{-41}{41}=- 1\).

Step1: Subtract 8 from both sides

Subtract 8 from both sides of the equation \(8|-9n - 9|+8 = 80\) to get \(8|-9n - 9|=80 - 8=72\).

Step2: Divide both sides by 8

Divide both sides by 8: \(|-9n - 9|=\frac{72}{8} = 9\).

Step3: Set up two equations

Since \(|x|=a\) implies \(x = a\) or \(x=-a\), we have two equations:

• Equation 1: \(-9n-9 = 9\)
• Equation 2: \(-9n-9=-9\)

Solve Equation 1:

Step1: Add 9 to both sides

Adding 9 to both sides: \(-9n=9 + 9=18\).

Step2: Divide by -9

Dividing by -9: \(n=\frac{18}{-9}=-2\).

Solve Equation 2:

Step1: Add 9 to both sides

Adding 9 to both sides: \(-9n=-9 + 9=0\).

Step2: Divide by -9

Dividing by -9: \(n = 0\).

Since we need to type the smaller value first, the smaller value is \(-2\) and the larger is \(0\).

Answer:

\(n = -1\)

Question 3