Answer: ![x=-1](https://tex.z-dn.net/?f=x%3D-1)
Step-by-step explanation:
By the negative exponent rule, you have that:
![(\frac{1}{a})^n=a^{-n}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7Ba%7D%29%5En%3Da%5E%7B-n%7D)
By the exponents properties, you know that:
![(m^n)^l=m^{(nl)}](https://tex.z-dn.net/?f=%28m%5En%29%5El%3Dm%5E%7B%28nl%29%7D)
Therefore, you can rewrite the left side of the equation has following:
![(\frac{1}{8})^{-(2x+7)}=(\frac{1}{32})^{3x}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B8%7D%29%5E%7B-%282x%2B7%29%7D%3D%28%5Cfrac%7B1%7D%7B32%7D%29%5E%7B3x%7D)
Descompose 32 and 8 into its prime factors:
![32=2*2*2*2*2=2^5\\8=2*2*2=2^3](https://tex.z-dn.net/?f=32%3D2%2A2%2A2%2A2%2A2%3D2%5E5%5C%5C8%3D2%2A2%2A2%3D2%5E3)
Rewrite:
![(\frac{1}{2^3})^{-(2x+7)}=(\frac{1}{2^5})^{3x}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B2%5E3%7D%29%5E%7B-%282x%2B7%29%7D%3D%28%5Cfrac%7B1%7D%7B2%5E5%7D%29%5E%7B3x%7D)
Then:
![(\frac{1}{2})^{-3(2x+7)}=(\frac{1}{2})^{5(3x)}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B-3%282x%2B7%29%7D%3D%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B5%283x%29%7D)
As the base are equal, then:
![-3(2x+7)=5(3x)](https://tex.z-dn.net/?f=-3%282x%2B7%29%3D5%283x%29)
Solve for x:
![-6x-21=15x\\-21=15x+6x\\-21=21x\\x=-1](https://tex.z-dn.net/?f=-6x-21%3D15x%5C%5C-21%3D15x%2B6x%5C%5C-21%3D21x%5C%5Cx%3D-1)
quita los paréntesis: 4x-5=2+3(x-3) multiplica paréntesis X3, elimina el paréntesis: 4x-5=2+3x-9 calcule: 4x-5= -7+3x mueve los términos y te quedará así: 4x-3x-5=-7
agrupe los términos semejantes: x=-7+5
calcular la suma, y el resultado final sería: x= -2
Step-by-step explanation:
espero te sirva