Inequality: solve 1/x+2>3

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jsh_aziza

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Dec 7, 2007
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I need to solve the following equation:

1/x+2>3

So far all I did on it was (1/x+2) -3>0 I am stuck though on what next to do. I know that if it was 1 lets say I can substitute x+2/x+2 for 1 and solve from there. Could someone please help me solve this? Thx. for your help.
 
jsh_aziza said:
1/x+2>3
Click to expand...
Does the left-hand side of the above mean "(1/x) + 2", "1/(x + 2)", or something else?

Thank you! :D

Eliz.
 
jsh_aziza said:
Sorry about that, the equation is (1/x+2)>3
Click to expand...
It's an inequality, not an equation (unless it's been posted incorrectly). And putting parentheses around the entire left-hand side does not, I'm afraid, answer the question: Is the left-hand side "(1/x) + 2", as you've posted it, or is it "1/(x + 2)", or is it something else?

Please reply with clarification, including a clear listing of your work and reasoning so far. Thank you.

Eliz.
 
If instead - you had an "=" sign - how would you have solved the problem?

Follow the same steps.
 
Subhotosh Khan said:
If instead - you had an "=" sign - how would you have solved the problem?

Follow the same steps.
Click to expand...
Not quite, I don't think...? If the "x" is in the denominator, then multiplying through would be fine for an equation, but is disallowed for an inequality. :oops:

Eliz.
 
stapel said:
Subhotosh Khan said:
If instead - you had an "=" sign - how would you have solved the problem?

Follow the same steps.
Click to expand...
Not quite, I don't think...? If the "x" is in the denominator, then multiplying through would be fine for an equation, but is disallowed for an inequality. :oops:
Eliz.
Click to expand...
Correct. I was incomplete in the solution instruction.

However, process is the same - just exclude the "root/s" of the denominator from the solution set. I was hoping the student would have found it - or the teacher in the class will have a discussion point.

Also in case the multiplying factor is negative - in this case x < -2 (i.e. multiplying by negative number) - the equality sign will be switched and a different solution set may need to be considered.
 
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