How do you solve #0.24y-0.64>3.86# and graph the solution on a number line?

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Answer 1 · 2017-10-02T16:30:35

See a solution process below:

First, add #color(red)(0.64)# to each side of the inequality to isolate the #y# term while keeping the inequality balanced:

#0.24y - 0.64 + color(red)(0.64) > 3.86 + color(red)(0.64)#

#0.24y - 0 > 4.5#

#0.24y > 4.5#

Now, divide each side of the inequality by #color(red)(0.24)# to solve for #y# while keeping the inequality balanced:

#(0.24y)/color(red)(0.24) > 4.5/color(red)(0.24)#

#(color(red)(cancel(color(black)(0.24)))y)/cancel(color(red)(0.24)) > 18.75#

#y > 18.75#

To graph this we will draw a horizontal line at #18.75# on the vertical axis.

The line will be a dashed line because the inequality operator does not contain an "or equal to" clause.

We will shade above the line because the inequality operator does contain a "greater than" clause:

graph{y> 18.75 [-50, 50, -5, 45]}