SOLUTION: graph the set of solution of each open sentence 1.)|2t+5|<7 2.)|w-5|>3

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Question 119350This question is from textbook Algebra and Trigonmertry structure and method
: graph the set of solution of each open sentence
1.)|2t+5|<7
2.)|w-5|>3 This question is from textbook Algebra and Trigonmertry structure and method

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
#1

Start with the given inequality

Break up the absolute value (remember, if you have , then and )

and Break up the absolute value inequality using the given rule

Combine the two inequalities to get a compound inequality

Subtract 5 from all sides

Divide all sides by 2 to isolate t

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Answer:

So our answer is

which looks like this in interval notation

if you wanted to graph the solution set, you would get

Graph of the solution set in blue and the excluded values represented by open circles

#2

Start with the given inequality

Break up the absolute value (remember, if you have , then or )

or Break up the absolute value inequality using the given rule

Now lets focus on the first inequality

Start with the given inequality

Add 5 to both sides

Combine like terms on the right side

Now lets focus on the second inequality

Start with the given inequality

Add 5 to both sides

Combine like terms on the right side

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Answer:

So our answer is

or

which looks like this in interval notation

if you wanted to graph the solution set, you would get

Graph of the solution set in blue and the excluded values represented by open circles