Question

1. 2(p - 1) - (9p - 2) = -6p - 4\\12) 9 - n + 12n + 11 = 2(11n - 1) - 6(6n - 12)

Explanation:

Problem 10: Solve \( 2(p - 1)-(9p - 2)=-6p - p \)

Step 1: Expand the left - hand side

First, use the distributive property \( a(b + c)=ab+ac \) to expand \( 2(p - 1) \) and \( -(9p - 2) \).
\( 2(p - 1)=2p-2 \) and \( -(9p - 2)=-9p + 2 \).
So the left - hand side becomes \( 2p-2-9p + 2 \).
Combine like terms: \( (2p-9p)+(-2 + 2)=-7p \).
The right - hand side: Combine like terms \( -6p-p=-7p \).
So the equation is \( -7p=-7p \).

Step 2: Analyze the solution

Since \( -7p=-7p \) is true for all real values of \( p \), the solution set is all real numbers.

Problem 12: Solve \( 9 - n+12n + 11=2(11n-1)-6(6n - 12) \)

Step 1: Simplify both sides

Left - hand side: Combine like terms.
\( 9+11+(-n + 12n)=20 + 11n \).
Right - hand side: Use the distributive property.
\( 2(11n-1)=22n-2 \) and \( -6(6n - 12)=-36n + 72 \).
Then combine like terms: \( 22n-2-36n + 72=(22n-36n)+(-2 + 72)=-14n+70 \).
So the equation is \( 11n + 20=-14n+70 \).

Step 2: Add \( 14n \) to both sides

\( 11n+14n + 20=-14n+14n+70 \)
\( 25n+20 = 70 \)

Step 3: Subtract 20 from both sides

\( 25n+20-20=70 - 20 \)
\( 25n=50 \)

Step 4: Divide both sides by 25

\( n=\frac{50}{25}=2 \)

Answer:

s:

• For problem 10: All real numbers.
• For problem 12: \( n = 2 \)