Question

1. find the solution to each equation mentally.

a. $30 + a = 40$
b. $500 + b = 200$
c. $-1 + c = -2$
d. $d + 3,567 = 0$

Explanation:

Part a: Solve \(30 + a = 40\)

To find \(a\), we need to isolate \(a\) by subtracting 30 from both sides of the equation. Mentally, we think "What number added to 30 gives 40?" Since \(40 - 30 = 10\), we have \(a = 10\).

Part b: Solve \(500 + b = 200\)

To find \(b\), we subtract 500 from both sides. Mentally, we consider "What number added to 500 gives 200?" Since \(200 - 500=- 300\), we get \(b=-300\).

Part c: Solve \(-1 + c=-2\)

To isolate \(c\), we add 1 to both sides. Mentally, we ask "What number added to - 1 gives - 2?" Since \(-2+1 = - 1\), we have \(c=-1\).

Part d: Solve \(d + 3567=0\)

To find \(d\), we subtract 3567 from both sides. Mentally, we think "What number added to 3567 gives 0?" Since \(0 - 3567=-3567\), we get \(d = - 3567\).

Answer:

a. \(a = 10\)

b. \(b=-300\)

c. \(c=-1\)

d. \(d=-3567\)