I need someone to help me with this problems: 6/v=3/11, 16j=320, 13x=15-2x.
As I understand, there are three unconnected equations, each with its own variable. Let's solve them one by one.
1) `6/v = 3/11.`
This is a proportion and we can use a rule for solving it, but it is probably better to solve it step by step. First, multiply both sides by `v` (it cannot be zero, so such a multiplication gives an equivalent equation):
`6 = 3/11*v.`
Then multiply by `11:` `6*11 = 3*v.`
And finally divide by `3` and compute: `v = (6*11)/3 = 2*11 = 22.`
2) `16 j=320.`
Only one step is here, divide both sides by `16` and note that `320=32*10=2*16*10:`
Two steps are here: first, add `2x` to both sides and obtain `13x+2x=15,` or `15 x=15.` Second, divide both sides by `15` and obviously `x=1.`
Another quick way to solve the first equation (so that you don't have to deal with fractions) is to cross-multiply. Anytime you have an equation that is just fraction=fraction, cross-multiplication is a great quick way to clean things up.
`6/v = 3/11` becomes `3v = 6*11` or `3v = 66`
We now have a simple, one-step equation to solve. Divide both sides by 3 and you get