Question

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Answer 1

Answer :

{ 1 , 2 , 3 , 4 , 5 }

To Find :

The solution of given inequality on the number line.

SolutioN :

$\tt \rightarrow \: - \frac{2}{3} \leq \dfrac{x}{3} \leq \dfrac{2}{3} , \: where \: x \: ∈ \: R.$

⚝ Taking Inequality 1.

$\tt \rightarrow \: - \frac{2}{3} \leq \dfrac{x}{3} - 1 .$

$\tt \rightarrow \: 1- \frac{2}{3} \leq \dfrac{x}{3} .$

$\tt \rightarrow \: 1 \leq x. \: \: \: - (1)$

⚝ Taking Inequality 2.

$\tt \rightarrow \: \frac{x}{3} - 1 \leq \dfrac{2}{3} .$

$\tt \rightarrow \: \frac{x}{3} \leq \dfrac{5}{3} .$

$\tt \rightarrow \: x \leq 5. \: \: \: -(2)$

From equation 1 and 2, we get.

•°• Solution of set is { 1 , 2 , 3 , 4 , 5 }

Answer 2

Step-by-step explanation:

Given :-

-2/3 ≤ (x/3)-1 ≤ 2/3 where x € R

To find :-

Solve the in-equation and graph the solution on the number line?

Solution :-

Given in-equation is -2/3 ≤ (x/3)-1 ≤ 2/3

On adding 1 both sides

=> (-2/3)+1 ≤ (x/3)-1+1 ≤ (2/3)+1

=> (-2+3)/3 ≤ (x/3)+0 ≤ (2+3)/3

=>(-2+3)/3 ≤ (x/3) ≤ (2+3)/3

=> 1/3 ≤ x/3 ≤ 5/3

On multiplying with 3 both sides then

=> 3(1/3) ≤ (x/3)×3 ≤ 3(5/3)

=> 3/3 ≤ 3x/3 ≤15/3

=> 1 ≤ x ≤5

The value of x lies between 1 ,2 , 3, 4, 5 (including 1 and 5)

Answer:-

The solution set for the in-equation is { 1,2,3,4,5}