Solve the given linear equation. − 6 = 3 5 t -6=\frac35t

Here we're asked to solve the given linear equation. We have negative six equals three fifths times T. Now remember, if we're dealing with a fraction coefficient, we can multiply by the reciprocal of that fraction in order to get it to cancel out. So since I have three fifths there, I want to get that T all by itself by multiplying by the reciprocal of three fifths, just flipping that fraction to get five thirds. Now, if I multiply by five thirds on one side, I have to multiply by five thirds on the other, So I also want to multiply this negative six by five thirds as well. Now, on this right hand side, this three fifths and five thirds will cancel out just leaving me with t and on this left hand side, I have five thirds times negative six. Now just multiplying those numerators across here because remember we can think of this negative six as being negative six over one, five times negative six will give me negative 30. Then that just gives me negative 30 over three multiplying those denominators across. Now I can do some further simplification because negative 30 is divisible by three. Negative 30 divided by three will give me negative 10 so I get my answer as negative 10 equals t. Now we can, of course, check our answer here by plugging that negative 10 back in for t to our original equation. So that would be negative six equals three fifths times negative 10. So going ahead and checking if this gives us a true statement doing this multiplication over here, negative six stays the same then focusing on this three fifths times negative 10. Three times negative 10 gives us negative 30 and that's over five here. Now negative 30 divided by five gives me negative six. So I end up with this statement that negative six equals negative six. This is of course a true statement as those are the same exact values so I know that I solved my equation correctly and that negative 10 is equal to t. Let me know if you have questions, and I'll see you in the next one.