Question

1. $12 + 5(x + 1)$
2. $12 - 5(x - 1)$

Explanation:

Problem 23: Simplify \( 12 + 5(x + 1) \)

Step 1: Distribute the 5

Using the distributive property \( a(b + c)=ab + ac \), we distribute 5 to \( x \) and 1.
\( 5(x + 1)=5x+5\times1 = 5x + 5 \)

Step 2: Combine like terms

Now we add 12 and the result from step 1.
\( 12+5x + 5=(12 + 5)+5x \)
\( 12+5 = 17 \), so we have \( 5x+17 \)

Step 1: Distribute the - 5

Using the distributive property \( a(b - c)=ab-ac \), we distribute - 5 to \( x \) and - 1.
\( - 5(x - 1)=-5x-5\times(-1)=-5x + 5 \)

Step 2: Combine like terms

Now we add 12 and the result from step 1.
\( 12-5x + 5=(12 + 5)-5x \)
\( 12 + 5=17 \), so we have \( - 5x+17 \) or \( 17-5x \)

Answer:

\( 5x + 17 \)

Problem 24: Simplify \( 12-5(x - 1) \)