Question

Solve and graph the solution set of

Answer 1

Please see the attachment

Answer 2

Given :-

2x- 9 < 7 and 3x + 9 ≤ 25, x ∈ R.

To find :-

x from 2x- 9 < 7 and 3x + 9 ≤ 25, x ∈ R.

Solution :-

Solving the first inequality,

=> 2x- 9 < 7     

=> 2x < 7 + 9    

=> 2x < 16

=> x < $\frac{16}{2}$      

=> x < 8                                                          .... (i.)

Now, solving the second inequality

⇒ 3x + 9 ≤ 25

⇒ 3x ≤ 25 - 9

⇒ 3x ≤ 16

⇒ x ≤ $\frac{16}{3}$

⇒ x ≤ 5.3                                                          .... (ii.)

From equation (i.) and (ii.) we get,

=> The required solution set is {x: x ≤ 5.3, x ∈ R}

Answer :-

x is from infinity (from negative side) to 5.3.

Graph :-

<---|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|---|----|-------|->

   -5     -4      -3      -2     -1       0       1        2      3       4       5  $^{5.3}$    6      7