Please help to solve this inequality

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May 2010
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The post reads: If you replace the equal sign of an equation with the inequality sign, there is never a time when the same value will be a solution to both, namely due to the fact that a solution less than or greater than never be equal to the same solution.

Solve: 6x + 7 > 15 x = 1 Can this be solved with the factor given for X. I do not think so, How am I suppose to solve this can someone help me to understand the steps that are needed to solve this inequality
 

skeeter

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Jun 2008
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The post reads: If you replace the equal sign of an equation with the inequality sign, there is never a time when the same value will be a solution to both, namely due to the fact that a solution less than or greater than never be equal to the same solution.

Solve: 6x + 7 > 15 x = 1 Can this be solved with the factor given for X. I do not think so, How am I suppose to solve this can someone help me to understand the steps that are needed to solve this inequality
I'm assuming the "equal sign" is a typo ... do you mean the inequality

\(\displaystyle 6x+7 > 15x+1\) ?

if so ...

subtract \(\displaystyle 6x\) and \(\displaystyle 1\) from both sides ...

\(\displaystyle 6 > 9x\)

divide both sides by \(\displaystyle 9\)

\(\displaystyle \frac{6}{9} > x\)

reduce and rewrite ...

\(\displaystyle x < \frac{2}{3}\)
 
Mar 2009
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Birmingham, Alabama.
Sorry. I didn't not recognize that the = sign would be a +. I agree with skeeter.
 
May 2010
52
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unfortunately I think that the student was trying to give the value of x=1 for the following
problem which read: 6x + 7 > 15 that is why I cannot figure it out. Can you please help?
 
May 2010
52
0
Correction for inequality question

This is the actual problem: 6x + 7 > 15

I need to know how to figure this out. The student had given the value of x to be 1. That just doesn't make sense to me.

Thank You!
 

pickslides

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Sep 2008
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Melbourne
\(\displaystyle 6x + 7 > 15\)

\(\displaystyle 6x + 7 {\color{red}-7}> 15{\color{red}-7}\)

\(\displaystyle 6x > 8\)

\(\displaystyle \frac{6x}{{\color{red}6}} > \frac{8}{{\color{red}6}}\)

\(\displaystyle x > \frac{8}{6} \approx 1.33\)
 
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Mar 2009
77
2
unfortunately I think that the student was trying to give the value of x=1 for the following
problem which read: 6x + 7 > 15 that is why I cannot figure it out. Can you please help?
The solution is the same as you would do for equation. If you had \(\displaystyle 6x +7 = 15\) how would you solve?

I guess you would do this.

\(\displaystyle 6x+7 = 15\)
\(\displaystyle
6x = 15-7\)

\(\displaystyle x = 8/6 = 4/3\)

Now it is the same for inequality.

\(\displaystyle 6x+7 > 15\) meanining \(\displaystyle 6x > 15-7\), meaning \(\displaystyle 6x > 8 \), meaning \(\displaystyle x > 4/3\)
 

skeeter

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Jun 2008
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North Texas
most probably, the longest thread I've seen over a linear inequality. (Wondering)
 
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