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How do you solve and graph #9 ( x - 11 ) > 17 + 7x#?

Answer 1

Julia Adams

#color(red)(x>58)#

#9(x−11)>17+7x#

#9x-99 >17+7x#

#9x-7x>17+99#

#2x>116#

#x>58#

Now, plot each graph separately and then shade the area that satisfies the inequality.

Your inequality is #9(x−11)>17+7x#

Your graph is

The blue area represents the region in which #9(x−11)>17+7x#

Check: Test a point in the coloured region.

Try (#150,1200#).

#9(x−11)>17+7x#
#9(150-11)>17+7(150)#
#9×139>17+1050#
#1251>1067#
∴ TRUE

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Answer 2

Avery Alexander

To solve and graph the inequality 9(x - 11) > 17 + 7x, follow these steps:

Distribute 9 across the parentheses: 9x - 99 > 17 + 7x
Subtract 7x from both sides to isolate the variable terms on one side: 9x - 7x - 99 > 17
Combine like terms: 2x - 99 > 17
Add 99 to both sides to isolate the variable term: 2x > 116
Divide both sides by 2 to solve for x: x > 58

The solution is x > 58.

To graph this inequality on a number line, plot an open circle at 58 (since the inequality is strict) and shade the region to the right of 58 to indicate all values greater than 58.

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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.

How do you solve and graph #9 ( x - 11 ) &gt; 17 + 7x#?

How do you solve and graph #9 ( x - 11 ) > 17 + 7x#?