Question

1. $-24 = 5r + 3r$
2. $-36 = 6(2 - 8n)$
3. $-14 = -(-2x + 2)$
4. $7(1 + 5n) + 6(1 + 4n) = 13$

Explanation:

Problem 3: $-24 = 5r + 3r$

Step1: Combine like terms

Combine the terms with \( r \) on the right side: \( 5r + 3r = 8r \), so the equation becomes \( -24 = 8r \).

Step2: Solve for \( r \)

Divide both sides by 8: \( r=\frac{-24}{8}=-3 \).

Step1: Distribute the 6

Multiply 6 into the parentheses: \( 6\times2 - 6\times8n = 12 - 48n \), so the equation is \( -36 = 12 - 48n \).

Step2: Subtract 12 from both sides

\( -36 - 12 = -48n \), which simplifies to \( -48 = -48n \).

Step3: Solve for \( n \)

Divide both sides by -48: \( n=\frac{-48}{-48}=1 \).

Step1: Distribute the negative sign

The negative sign outside the parentheses changes the signs inside: \( -1\times(-2x)+(-1)\times2 = 2x - 2 \), so the equation is \( -14 = 2x - 2 \).

Step2: Add 2 to both sides

\( -14 + 2 = 2x \), which simplifies to \( -12 = 2x \).

Step3: Solve for \( x \)

Divide both sides by 2: \( x=\frac{-12}{2}=-6 \).

Answer:

\( r = -3 \)

Problem 5: $-36 = 6(2 - 8n)$