How do you solve and graph #8r+6<9r#?

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Answer 1 · 2017-08-11T12:00:27

See a solution process below:

Subtract #color(red)(8r)# from each side of the inequality to solve for #r# while keeping the inequality balanced:

#-color(red)(8r) + 8r + 6 < -color(red)(8r) + 9r#

#0 + 6 < (-color(red)(8) + 9)r#

#6 < 1r#

#6 < r#

Or, to state the solution in terms of #r# we can reverse or "flip" the entire inequality:

#r > 6#

Answer 2 · 2017-08-11T12:21:46

#=>r>6#

graph{x>6 [-16.02, 16.01, -8.01, 8.01]}

#8r+6<9r#

Subtract #8r# from both sides

#=>8rcolor(red)(-8r)+6<9rcolor(red)(-8r)#

#=>6<# #r#

#=>r>6#

The shaded part in the graph is #r>6.#
graph{x>6 [-16.02, 16.01, -8.01, 8.01]}