Question

2. Mark each of the following sentences as true or false.
(a) If ax +b >c then ax >c-b.
c-b
(b) If ax +b >c then x < where a is a negative number.
(c) If a > b then a-c>b-c.
(d) If a <b then ac <bc,c +0.
b
(e) If a > b then - >-, C 0.
(f) If a-c<b-d then a + d <b+c.
C
C​

Answer 1

If ax +b > c then ax >c-b is a false statement

If ax +b >c then x < a where a is a negative number true statement

If a > b then a-c > b-c is a true statement

If a < b then ac < bc is a true statement

If a > b then - > - is a false statement

If a-c < b-d then a + d < b+c is a false statement

     

Given:  

(a) If ax +b > c then ax >c-b.

(b) If ax +b > c then x < where a is a negative number.

(c) If a > b then a-c > b - c

(d) If a < b then ac < bc, c + 0

(e) If a > b then - > -, C 0

(f)  If a - c < b - d then a + d < b+c

To find:

Mark each of the following sentences as true or false.

Solution:

(a)  If ax +b > c then ax >c-b.

The above statement is false

Since the inequality ax > c - b is not true if ax + b > c.

For example, if a = 2, b = 3, and c = 3,

then ax + b > c =>  2x + 3 > 3  which is false  

∴ If ax +b > c then ax >c-b is a false statement

(b) If ax +b >c then x < a where a is a negative number.

The above statement is true  

if ax + b > c and a is a negative number,

then x is less than c - b

For example, if a = -2, b = 3, and c = 5,

then ax + b > c =>   -2x + 3 > 5 is true

∴ If ax +b >c then x < a where a is a negative number true statement

(c) If a > b then a-c > b-c.

The above statement is true  

For example, if a = 4, b = 3, and c = 2, then

=> a > b = 4 > 3 is true  

=> a-c > b-c =  4 - 2 > 3 - 2 = 2 > 1 which is true

∴ If a > b then a-c > b-c is a true statement

(d) If a < b then ac < bc, c + 0

The above statement is true  

For example, if a = 2, b = 1, and c = 3, then

=> a > b = 2 > 1 is true  

=> ac < bc =  6 < 3  which is true

∴ If a < b then ac < bc is a true statement

(e) If a > b then - > -, C  

The above statement is false because ' - > - ' is not a valid statement.

∴ If a > b then - > - is a false statement

(f) If a-c < b-d then a + d < b+c.

The above statement is false

The inequality a + d < b + c is not certainly true if a-c < b-d.

For example, take a = 1, b = 2, c = 3, and d = 4, then

Then a - c < b - d =>  1 - 3 < 2 - 4 is false

but a + d < b + c =>  2 + 5 < 3 + 4 is is ture  

∴  If a-c < b-d then a + d < b+c is a false statement

Therefore,

If ax +b > c then ax >c-b is a false statement

If ax +b >c then x < a where a is a negative number true statement

If a > b then a-c > b-c is a true statement

If a < b then ac < bc is a true statement

If a > b then - > - is a false statement

If a-c < b-d then a + d < b+c is a false statement

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