1.

Take as x different positive numbers, negative numbers and zero, and compute x + 1, x – 1, 1 – x. Check whether the equations below hold for all numbers.i. (1 + x) + (1 – x) = 2ii. x – (x – 1) = 1iii. 1 – x = -(x – 1)

Answer»

If x = 1

x + 1 = 1 + 1 = 2

x – 1 = 1 – 1 = 0

1 – x = 1 – 1 = 0

If x = 2

x + 1 = 2 + 1 = 3

x – 1 = 2 – 1 = 1

1 – x = 1 – 2 – 1

If x = 0

x + 1 = 0 + 1

x – 1 = 0 – 1 = -1

1 – x = 1 – 0 = 1

If x = -1

x + 1 = -1 + 1 = 1 – 1 = 0

x – 1 = -1 – 1 = -2

1 – x = 1 – (-1) = 1 + 1 = 2

If x = -2

x + 1 = -2 + 1 = -1

x – 1 = -2 – 1 = -3

1 – x = 1 – (-2) = 1 + 2 = 3

i. (1 + x) + (1 – x)

In x = 1, (1 + x) + (1 – x) = 2 + 0 = 2

In x = 2, (1 + x) + (1 – x) = 3 + (-1) = 3 – 1 = 2

In x = 0, (1 + x) + (1 – x) = 1 + 1 = 2

In x = -1, (1 + x) + (1 – x) = 0 + 2 = 2

In x – 2, (1 + x) + (1 – x) – 1 + 3 = 3 – 1 = 2

(1 + x) + (1 – x) = 2 , for all values of x

ii. x – (x – 1)

In x = 1, x – (x – 1) = 1 – 0 = 1

In x = 2, x – (x – 1) = 2 – 1 = 1

In x = 0, x – (x – 1) = 0 – (-1) = 1

In x = -1, x – (x – 1) = -1 – (-2) = -1 + 2 = 1

In x = -2, x – (x – 1) = -2 – (-3) = -2 + 3 = 1

x – (x – 1) = 1, for all values of x

iii. 1 – x

In x = 1, 1 – x = o = -(x – 1)

In x = 2, 1 – x = -1 = -(1) = -(x – 1)

In x = o, 1 – x = 1 = -(-1) = -(x – 1)

In x = -1, 1 – x = 2 = -(-2) = -(x – 1)

In x = -2, 1 – x = 3 = -(-3) = -(x – 1)

1 – x = -(x – 1), for all values of x


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