+0

# Help me

0
307
2

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

|0.7x+5|>6.7

Sep 22, 2017

#2
+2339
+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:

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

.
Sep 22, 2017

#1
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

Sep 22, 2017
#2
+2339
+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