List the elements of the solution set of the inequation $- 3 < x - 2 \leq 9 - 2 x; x \in N$

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Solution

Given: $- 3 < x - 2 \leq 9 - 2 x$

$\Rightarrow - 3 < x - 2 and x - 2 \leq 9 - 2 x$

$\Rightarrow - 3 + 2 < x and x + 2 x \leq 9 + 2$

$\Rightarrow x > - 1 and 3 x \leq 11$

$\Rightarrow x > - 1 and x \leq 11 / 3$

Since x $\in$ N,

Elements of solution set are { 1, 2, 3 }.

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List the elements of the solution set of the inequation −3 < x−2 ≤ 9−2x ; x∈ N

Given: −3 < x−2 ≤ 9−2x ⇒ −3 < x−2 and x−2≤ 9−2x ⇒ −3+2 < x and x+2x≤ 9+2 ⇒ x > −1 and 3x≤ 11 ⇒ x > −1 and x≤ 11/3 Since x ∈ N, Elements of solution set are { 1, 2, 3 }.

List the elements of the solution set of the inequation $- 3 < x - 2 \leq 9 - 2 x; x \in N$

Given: $- 3 < x - 2 \leq 9 - 2 x$

$\Rightarrow - 3 < x - 2 and x - 2 \leq 9 - 2 x$

$\Rightarrow - 3 + 2 < x and x + 2 x \leq 9 + 2$

$\Rightarrow x > - 1 and 3 x \leq 11$

$\Rightarrow x > - 1 and x \leq 11 / 3$

Since x $\in$ N,

Elements of solution set are { 1, 2, 3 }.