Step-by-step explanation:
It's not rocket science. What we need to do is simply 'cross-multiply' them and then do the rest calculations. So, what's provided as per given problem is "9/x = -3/10". As I said in the beginning, we just need to cross multiply them to reach to our destination.
Let's proceed!
[tex]\implies{\sf{9/x = -3/10}}[/tex]
On cross-multplying we get,
[tex]\implies{\sf{9(10) = -3(x)}}[/tex]
Solve the brackets,
[tex]\implies{\sf{90 = -3x}}[/tex]
Divide by 3 on both sides,
[tex]\implies{\sf{90/3 = -3x/3}}[/tex]
[tex]\implies{\sf{30 = -x}}[/tex]
[tex]\implies{\sf{-x = 30}}[/tex]
[tex]\implies{\sf{x=-30}}[/tex]
Therefore, the value of x is - 30.
The other way to solve this problem is first cut the divisible term. In simple words 9 is divisible of 3. So, at this time our equation looks like: 3/x = -1/10. Again cross multiply them. Cross-multiplication is the key to solve such questions!
[tex]\implies{\sf{3/x = -1/10}}[/tex]
[tex]\implies{\sf{3(10) = -1(x)}}[/tex]
[tex]\implies{\sf{30 = -x}}[/tex]
[tex]\implies{\sf{x=-30}}[/tex]