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

Answer 1

See a solution process below:

To find #r# while maintaining the balance of the inequality, subtract #color(red)(8r)# from each side of the inequality:

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

(-color(red)(8) + 9)r# = #0 + 6
#6 < 1r#
#6 < r#
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Answer 2

#=>r>6#

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

#8r+6<9r#
Take #8r# away from both sides.
#=>8<9~color(red)(-8r)#=8rcolor(red)(-8r)+6
#=>6<# #r#
#=>r>6#
In the graph, #r>6.# graph{x>6 [-16.02, 16.01, -8.01, 8.01]} is the shaded area.
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Answer 3

To solve and graph the inequality (8r + 6 < 9r), first, subtract (8r) from both sides to isolate (r) on one side of the inequality. Then, subtract 6 from both sides. Finally, graph the solution on a number line.

[ \begin{align*} 8r + 6 &< 9r \ 6 &< 9r - 8r \ 6 &< r \end{align*} ]

On a number line, draw an open circle at 6 (because the inequality is less than, not less than or equal to), then shade to the right since (r) is greater than 6.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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