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i need help with this problem so can you help me please 

 

 

|0.7x+5|>6.7

Guest Sep 22, 2017

Best Answer 

 #2
avatar+1493 
+1

Absolute value inequalities are not that simple! You can't simply just ignore them.

 

\(|0.7x+5|>6.7\) The absolute value always splits your answer into the positive and negative answer.
\(0.7x+5>6.7\) \(-(0.7x+5)>6.7\)

 

Now that the absolute value has been accounted for, we should now solve for x in both equations.
\(7x+50>67\) \(0.7x+5<-6.7\)

 

Dividing by -1 causes a flipflop of the inequality sign.
\(7x+50>67\) \(7x+50<-67\)

 

Subtract 50 on both sides.
\(7x>17\) \(7x<-117\)

 

Divide by 7 on both sides.
\(x>\frac{17}{7}\) \(x<-\frac{117}{7}\)

 

 
   

 

This is your answer. Since the greater than symbol will cause an "or" statement, we know that solutions are the following:

 

\(x>\frac{17}{7}\hspace{1mm}\text{or}\hspace{1mm} x<-\frac{117}{7}\)

TheXSquaredFactor  Sep 22, 2017
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2+0 Answers

 #1
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0

|0.7x+5|>6.7   Remove the absolute value

 

0.7x + 5 > 6.7  subtract 5 from both sides

0.7x > 1.7          divide both sides by 0.7

x > 2.42857

Guest Sep 22, 2017
 #2
avatar+1493 
+1
Best Answer

Absolute value inequalities are not that simple! You can't simply just ignore them.

 

\(|0.7x+5|>6.7\) The absolute value always splits your answer into the positive and negative answer.
\(0.7x+5>6.7\) \(-(0.7x+5)>6.7\)

 

Now that the absolute value has been accounted for, we should now solve for x in both equations.
\(7x+50>67\) \(0.7x+5<-6.7\)

 

Dividing by -1 causes a flipflop of the inequality sign.
\(7x+50>67\) \(7x+50<-67\)

 

Subtract 50 on both sides.
\(7x>17\) \(7x<-117\)

 

Divide by 7 on both sides.
\(x>\frac{17}{7}\) \(x<-\frac{117}{7}\)

 

 
   

 

This is your answer. Since the greater than symbol will cause an "or" statement, we know that solutions are the following:

 

\(x>\frac{17}{7}\hspace{1mm}\text{or}\hspace{1mm} x<-\frac{117}{7}\)

TheXSquaredFactor  Sep 22, 2017

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