Question

If the replacement set is the set of natural numbers, solve: 3x – 4 > 6​

Answer 1

(i) x – 5 < 0

x – 5 + 5 < 0 + 5 ………(Adding 5)

=> x < 5

Required answer = {1, 2, 3, 4}

(ii) x + 1 ≤ 7 = > x + 1 – 1 ≤ 7 – 1 (Subtracting 1)

=> x ≤ 6

Required answer = {1, 2, 3, 4, 5, 6}

(iii) 3x – 4 > 6

3x – 4 + 4 > 6 + 4 (Adding 4)

=> 3x > 10

\frac { 3x }{ 3 } > \frac { 10 }{ 3 } …(Dividing by 3)

=> x > \frac { 10 }{ 3 }

=> x > 3\frac { 1 }{ 3 }

Required answer = { 4, 5, 6, …}

(iv) 4x + 1 ≥ 17

=> 4x + 1 – 1 ≥ 17 – 1 (Subtracting)

=> 4x ≥ 16

=> \frac { 4x }{ 4 } ≥ \frac { 16 }{ 4 } (Dividing by 4)

=> x ≥ 4

Required answer = {4, 5, 6, …}

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