Question

solve the following equations.
a. $x + 4 = 1$
b. $^{-}5 + x = ^{-}4$
c. $^{-}x = 2$
a. the solution is \boxed{}. (simplify your answer.)
b. the solution is \boxed{}. (simplify your answer.)
c. the solution is \boxed{}. (simplify your answer.)

Explanation:

Part a:

Step1: Isolate \( x \) by subtracting 4.

To solve \( x + 4 = 1 \), we subtract 4 from both sides of the equation. This is based on the subtraction property of equality, which states that if we subtract the same number from both sides of an equation, the equality still holds.
So, \( x + 4 - 4=1 - 4 \)

Step2: Simplify both sides.

Simplifying the left side, \( x+4 - 4=x \). Simplifying the right side, \( 1-4=- 3 \). So we get \( x=-3 \)

Part b:

Step1: Isolate \( x \) by adding 5.

To solve \( - 5+x=-4 \), we add 5 to both sides of the equation. This is based on the addition property of equality, which states that if we add the same number to both sides of an equation, the equality still holds.
So, \( -5 + x+5=-4 + 5 \)

Step2: Simplify both sides.

Simplifying the left side, \( - 5+x + 5=x \). Simplifying the right side, \( -4 + 5 = 1 \). So we get \( x = 1 \)

Part c:

Step1: Isolate \( x \) by multiplying by - 1.

To solve \( -x=2 \), we multiply both sides of the equation by - 1. This is based on the multiplication property of equality, which states that if we multiply both sides of an equation by the same non - zero number, the equality still holds.
So, \( (-1)\times(-x)=(-1)\times2 \)

Step2: Simplify both sides.

Simplifying the left side, \( (-1)\times(-x)=x \). Simplifying the right side, \( (-1)\times2=-2 \). So we get \( x=-2 \)

Answer:

a. The solution is \(-3\)
b. The solution is \(1\)
c. The solution is \(-2\)