Question

assignment
solve each equation.

1. $-31 = x + -13$

1. $-5 = k + 1$

1. $-12 = -4 - k$

1. $2 + n = -10 - 2n$

1. $-5b - 1 + 8 = -8b - 11$

Explanation:

Problem 1: $-31 = x + -13$

Step1: Add 13 to both sides

To isolate \( x \), we add 13 to both sides of the equation. This is based on the addition property of equality, which states that if \( a = b \), then \( a + c = b + c \).
\[
-31 + 13 = x + (-13) + 13
\]

Step2: Simplify both sides

Simplify the left - hand side: \( -31+13=-18 \).
Simplify the right - hand side: \( x+(-13) + 13=x+( - 13 + 13)=x+0=x \)

Step1: Subtract 1 from both sides

Using the subtraction property of equality (if \( a = b \), then \( a - c=b - c \)), we subtract 1 from both sides to isolate \( k \).
\[
-5-1=k + 1-1
\]

Step2: Simplify both sides

Simplify the left - hand side: \( -5-1=-6 \).
Simplify the right - hand side: \( k+1 - 1=k+0 = k \)

Step1: Add 4 to both sides

Using the addition property of equality, add 4 to both sides of the equation.
\[
-12 + 4=-4 - k+4
\]

Step2: Simplify both sides

Simplify the left - hand side: \( -12 + 4=-8 \).
Simplify the right - hand side: \( -4 - k+4=-k+( - 4 + 4)=-k+0=-k \)
So we have \( -8=-k \)

Step3: Multiply both sides by - 1

Multiply both sides of the equation \( -8=-k \) by - 1 to solve for \( k \).
\[
(-1)\times(-8)=(-1)\times(-k)
\]

Step4: Simplify both sides

Simplify the left - hand side: \( (-1)\times(-8) = 8 \)
Simplify the right - hand side: \( (-1)\times(-k)=k \)

Answer:

\( x=-18 \)

Problem 3: $-5 = k + 1$