For the first equation:
When x=-5
![2x+3n](https://img.qammunity.org/2023/formulas/mathematics/college/uz1s4ajnc3koi22whjr2i9tam5f67z1tc3.png)
![2(-5)+3n](https://img.qammunity.org/2023/formulas/mathematics/college/s49de0y25hpqy2t1owey3vrnl0va4fpyx5.png)
![-10+3n](https://img.qammunity.org/2023/formulas/mathematics/college/4esf00jfgp2z0ffii59dmgqi7wayzg1yn4.png)
When x=-1
![2x+3n_{}](https://img.qammunity.org/2023/formulas/mathematics/college/2kpritn6k2mfnpgohb688mbxej6j5nn6mr.png)
![2(-1)+3n](https://img.qammunity.org/2023/formulas/mathematics/college/87meejgnnqabmg3wt1cvtszj08n0kx4vaq.png)
![-2+3n](https://img.qammunity.org/2023/formulas/mathematics/college/bc6q0j67q471d3ko0vh05fdjhrqr7ex9zd.png)
For the second equation:
When x=5
![2x^2-3x-9](https://img.qammunity.org/2023/formulas/mathematics/college/hv8kwlrq1szfyi1tael1hpr47qskk2ujdi.png)
![2(5)^2-3(5)-9](https://img.qammunity.org/2023/formulas/mathematics/college/4tpzivs3laxgkallt7qz65oqva063f1ehl.png)
![50-15-9](https://img.qammunity.org/2023/formulas/mathematics/college/edj6yxzp1zpaymv47nlpvlm9k1n3tqeevt.png)
![=26](https://img.qammunity.org/2023/formulas/mathematics/middle-school/enot7x9dx59cykmzlxsw3vmqxy80y9mm3r.png)
when x=-1
![2x^2-3x-9](https://img.qammunity.org/2023/formulas/mathematics/college/hv8kwlrq1szfyi1tael1hpr47qskk2ujdi.png)
![2(-1)^2-3(-1)-9](https://img.qammunity.org/2023/formulas/mathematics/college/i43nkr2v1sth7hmyf5zf8dypivi53bd1b2.png)
![2+3-9](https://img.qammunity.org/2023/formulas/mathematics/college/8zcfm3n60lori6699dc7dttqroev1670v2.png)
![=-4](https://img.qammunity.org/2023/formulas/mathematics/college/f61bng13t6qvispklf8xlj660guf7xyfqr.png)
Now, we need to know the value for n to make the function continues:
We need to find when:
Lim when x tends to a of f(x)= f(-1)
Lim when x tends to -1 (negative)=-4
Lim when x tends to -1(positive) of -2+3n=-4
Solve for n :
-2+3n = -4
3n = -4+2
3n = -2
n=-2/3