How do you solve #\frac { 5\cdot 3y } { 2} > 2y - 1#?

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Answer 1 · 2017-07-16T13:04:38

See a solution process below:

First, calculate the result of the expression in the denominator of the fraction on the left side of the inequality:

#(15y)/2 > 2y - 1#

Next, multiply each side of the inequality by #color(red)(2)# to eliminate the fraction while keeping the inequality balanced:

#color(red)(2) xx (15y)/2 > color(red)(2)(2y - 1)#

#cancel(color(red)(2)) xx (15y)/color(red)(cancel(color(black)(2))) > (color(red)(2) xx 2y) - (color(red)(2) xx 1)#

#15y > 4y - 2#

Then, subtract #color(red)(4y)# from each side of the inequality to isolate the #y# term while keeping the inequality balanced:

#-color(red)(4y) + 15y > -color(red)(4y) + 4y - 2#

#(-color(red)(4) + 15)y > 0 - 2#

#11y > -2#

Now, divide each side of the inequality by #color(red)(11)# to solve for #y# while keeping the inequality balanced:

#(11y)/color(red)(11) > -2/color(red)(11)#

#(color(red)(cancel(color(black)(11)))y)/cancel(color(red)(11)) > -2/11#

#y > -2/11#