How do you solve #15y - \frac { 11} { 2} = \frac { 11} { 2} y + 2#?

Question

Genesis Allen · Accepted Answer

You can save yourself some trouble and a possible source of error by multiplying everything by #2# #->30y-11=11y+4# Now move the #y#'s to one side, and the numbers to the other, by subtracting #11y# from both sides and adding #11#: #->30y-cancel11-11y+cancel11=cancel(11y)+4-cancel(11y)+11# #->19y=15->y=15/19#

Avery Alexander · Answer

#y=15/19#

#"to eliminate the fractions multiply ALL terms by 2 the"# #"denominator of the fractions"#

#(2xx15y)-(cancel(2)^1xx11/cancel(2)^1)=(cancel(2)^1xx(11y)/cancel(2)^1)+(2xx2)#

#rArr30y-11=11y+4larrcolor(red)" no fractions"#

#"subtract 11y from both sides"#

#30y-11y-11=cancel(11y)cancel(-11y)+4#

#rArr19y-11=4#

#"add 11 to both sides"#

#19ycancel(-11)cancel(+11)=4+11#

#rArr19y=15#

#"divide both sides by 19"#

#(cancel(19) y)/cancel(19)=15/19#

#rArry=15/19#

#color(blue)"As a check"#

Substitute this value into the equation and if left side equals right side then it is the solution.

#"left "=(15xx15/19)-11/2=225/19-11/2=241/38#

#"right "=(11/2xx15/19)+2=165/38+2=241/38#

#rArry=15/19" is the solution"#

Eva Abramson · Answer

undefined To solve the equation $ 15y - \frac{11}{2} = \frac{11}{2}y + 2 $, you can follow these steps:

Step 1: Move all terms involving $ y $ to one side of the equation and the constant terms to the other side. You can do this by adding or subtracting terms as necessary. In this case, let's subtract $ \frac{11}{2}y $ from both sides and add $ \frac{11}{2} $ to both sides:

$$ 15y - \frac{11}{2} - \frac{11}{2}y = 2 + \frac{11}{2} $$

Step 2: Simplify both sides of the equation:

$$ 15y - \frac{11}{2} - \frac{11}{2}y = 2 + \frac{11}{2} $$
$$ (15y - \frac{11}{2}y) = (2 + \frac{11}{2}) $$

Step 3: Combine like terms:

$$ (\frac{15}{2}y) = (\frac{25}{2}) $$

Step 4: Now, isolate $ y $ by dividing both sides of the equation by $ \frac{15}{2} $:

$$ y = \frac{\frac{25}{2}}{\frac{15}{2}} $$

Step 5: Simplify the expression:

$$ y = \frac{25}{2} \times \frac{2}{15} $$
$$ y = \frac{25}{15} $$

Step 6: Simplify the fraction:

$$ y = \frac{5}{3} $$

So, the solution to the equation is $ y = \frac{5}{3} $.