Question

1. $-12r + 4 = 100$
2. $-7 + 4r = -15$

Explanation:

Problem 3: $-12r + 4 = 100$

Step 1: Subtract 4 from both sides

To isolate the term with \( r \), we subtract 4 from both sides of the equation. This gives us:
\( -12r + 4 - 4 = 100 - 4 \)
Simplifying both sides, we get:
\( -12r = 96 \)

Step 2: Divide by -12

To solve for \( r \), we divide both sides of the equation by -12:
\( \frac{-12r}{-12} = \frac{96}{-12} \)
Simplifying, we find:
\( r = -8 \)

Problem 4: $-7 + 4r = -15$

Step 1: Add 7 to both sides

To isolate the term with \( r \), we add 7 to both sides of the equation:
\( -7 + 4r + 7 = -15 + 7 \)
Simplifying both sides, we get:
\( 4r = -8 \)

Step 2: Divide by 4

To solve for \( r \), we divide both sides of the equation by 4:
\( \frac{4r}{4} = \frac{-8}{4} \)
Simplifying, we find:
\( r = -2 \)

Answer:

s:
Problem 3: \( \boldsymbol{r = -8} \)
Problem 4: \( \boldsymbol{r = -2} \)