Question

Solve the inequalities for the following: $7\leq \frac{(3x+11)}{2} \leq 11$

Answer 1

Answer:

1 ≤ x ≤  11/3

x = 1 , 2 , 3  (integral values)

Step-by-step explanation:

7 ≤ (3x + 11)/2  ≤ 11

multiplying by 2 both sides

=> 2 * 7  ≤ 2 * (3x + 11)/2  ≤  2 *11

=> 14 ≤ 3x + 11  ≤  22

subtracting 11 from both sides

=> 14 - 11 ≤ 3x + 11 - 11 ≤  22 - 11

=> 3 ≤ 3x ≤  11

Diving by 3 on both sides

=> 1 ≤ x ≤  11/3

if we talk about ingral values only

then x = 1 , 2 , 3

Answer 2

Answer:

$1 \leq x \leq \frac{11}{3}$

x = 1 , 2 , 3  (integral values)

Step-by-step explanation:

In this question

We have been given that

$7 \leq \frac{(3x + 11)}{2}\leq 11$

Multiplying by 2 both sides

=> $2\times 7 \leq 2\times \frac{(3x + 11)}{2}\leq2\times 11$

=> 14 ≤ 3x + 11  ≤  22

Subtracting 11 from both sides

=> 14 - 11 ≤ 3x + 11 - 11 ≤  22 - 11

=> 3 ≤ 3x ≤  11

Diving by 3 on both sides

=> 1 ≤ x ≤  11/3

If we talk about  values only

Then x = 1 , 2 , 3

Hence, 1 ≤ x ≤  11/3

            x = 1 , 2 , 3