Question

1. $-120 = 2(4 + 8p)$
2. $128 = 4(5x + 2)$
3. $6(-7 + 2p) - 6p = -90$
4. $8(b + 3) = 88$
5. $-2n - 2(8 + 6n) = -100$
6. $-100 = -4(1 - 3p)$

Explanation:

Problem 25: $-120 = 2(4 + 8p)$

Step 1: Divide both sides by 2

To isolate the term with \( p \), we divide both sides of the equation by 2.
\( \frac{-120}{2} = \frac{2(4 + 8p)}{2} \)
\( -60 = 4 + 8p \)

Step 2: Subtract 4 from both sides

Subtract 4 from both sides to get the term with \( p \) alone on one side.
\( -60 - 4 = 8p \)
\( -64 = 8p \)

Step 3: Divide by 8

Divide both sides by 8 to solve for \( p \).
\( \frac{-64}{8} = p \)
\( p = -8 \)

Step 1: Divide both sides by 4

Divide both sides by 4 to simplify the equation.
\( \frac{128}{4} = 5x + 2 \)
\( 32 = 5x + 2 \)

Step 2: Subtract 2 from both sides

Subtract 2 from both sides to isolate the term with \( x \).
\( 32 - 2 = 5x \)
\( 30 = 5x \)

Step 3: Divide by 5

Divide both sides by 5 to solve for \( x \).
\( \frac{30}{5} = x \)
\( x = 6 \)

Step 1: Distribute the 6

Distribute the 6 across the terms inside the parentheses.
\( 6(-7) + 6(2p) - 6p = -90 \)
\( -42 + 12p - 6p = -90 \)

Step 2: Combine like terms

Combine the \( p \)-terms.
\( -42 + 6p = -90 \)

Step 3: Add 42 to both sides

Add 42 to both sides to isolate the term with \( p \).
\( 6p = -90 + 42 \)
\( 6p = -48 \)

Step 4: Divide by 6

Divide both sides by 6 to solve for \( p \).
\( p = \frac{-48}{6} \)
\( p = -8 \)

Answer:

\( p = -8 \)

Problem 26: \( 128 = 4(5x + 2) \)