How do you graph #7/3x <7#?

1 Answer
smendyka
Jan 14, 2018

See a solution process below:

Explanation:

Multiply each side of the inequality by #color(red)(3)/color(blue)(7)# to solve for #x# while keeping the inequality balanced:

#color(red)(3)/color(blue)(7) xx 7/3x < color(red)(3)/color(blue)(7) xx 7#

#cancel(color(red)(3))/cancel(color(blue)(7)) xx color(blue)(cancel(color(black)(7)))/color(red)(cancel(color(black)(3)))x < color(red)(3)/cancel(color(blue)(7)) xx color(blue)(cancel(color(black)(7)))#

#x < 3#

To graph this we will draw a vertical line at #3# on the horizontal axis.

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

We will shade to the left side of the line because the inequality operator contains a "less than" clause:

graph{x < 3 [-10, 10, -5, 5]}

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