# Inequality problem

• Sep 18th 2012, 05:45 PM
itgl72
Inequality problem
The following problem raises some questions to me as to how the answer came to be:

7(x+4) (greater than or equal) 6(x-3)+x

After going through the problem I end up with an answer of:

0 is (greater than or equal) to -46

Not sure whats happening here because when I look up the answer I see it charted on the line from end to end going outward and an answer of

(-infinity sign, infinity sign)
• Sep 18th 2012, 06:54 PM
yeikel
Re: Inequality problem
There are no solution for this equation since 46 can be equal to 0
• Sep 18th 2012, 07:01 PM
Prove It
Re: Inequality problem
Quote:

Originally Posted by itgl72
The following problem raises some questions to me as to how the answer came to be:

7(x+4) (greater than or equal) 6(x-3)+x

After going through the problem I end up with an answer of:

0 is (greater than or equal) to -46

Not sure whats happening here because when I look up the answer I see it charted on the line from end to end going outward and an answer of

(-infinity sign, infinity sign)

\displaystyle \begin{align*} 7(x + 4) &\geq 6(x - 3) + x \\ 7x + 28 &\geq 6x - 18 + x \\ 7x + 28 &\geq 7x - 18 \\ 28 &\geq -18 \end{align*}

This final statement is true no matter what the value of x, so the original inequality holds true for all x. So the solution is \displaystyle \begin{align*} x \in (-\infty, \infty) \end{align*}.