Do the math the same way you would if all the other variables were numbers. For linear equations such as these, you can • subtract one side of the equation, so you get an equation equal to zero. • factor out the variable of interest • subtract all terms that don't have the variable as a factor • divide by the coefficient of the variable.
19. 2xy - x - 7 = 0 . . . . subract the right side x(2y-1) -7 = 0 . . . . factor out x x(2y -1) = 7 . . . . subtract the term(s) not containing x. Subtract -7 here. x = 7/(2y -1) . . . . divide by the coefficient of x
20. Usually for these, you would eliminate fractions first. (You don't have to, but it does simplify things a bit.) 2d + f = 24 . . . . multiply the equation by 4 to eliminate fractions f = 24 - 2d . . . . subtract the term not involving f
21. We can go back to the above sequence of steps here, if you like. 3(2j -k) -108 = 0 . . . . subtract the right side 6j -3k -108 = 0 . . . . separate the j terms from the others (eliminate parentheses using the distributive property) 6j = 108 + 3k . . . . add the opposite of the non-j terms j = 108/6 + 3k/6 . . . . divide by the coefficient of j j = 18 + k/2 . . . . simplify
22. "solve for" variable not specified. t = (3.5s -42)/4 s = (4t+42)/3.5 In both cases, the 3.5 can be replaced by 7/2 and the fraction simplified. t = (7/8)(s-12) s = 12 + (8/7)t
