Answer:
x = -10
Step-by-step explanation:
-x + 1 = x + 21
(given)
__________
-x + 1 = x + 21
+x +x
(addition property of equality)
(add the x term on both sides to cancel out -x)
__________
1 = 2x + 21
-21 -21
(subtraction property of equality)
(subtract by 21 on both sides to get rid of the constant term on the x side)
________
-20 = 2x
÷2 ÷2
(division property of equality)
(divide to get rid of the coefficient of 2 in the x term)
_______
-10 = x
(symmetric property of equality)
(switch both sides so that x is on the left)
_______
x = -10
________________________________
Proof by substitution:
x = -10 because
x = -10 → -x + 1 = x + 21 → -(x) + 1 = (x) + 21 → -(-10) + 1 = (-10) + 21 → 10 + 1 = 21 - 10 →
11 = 11
