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Solve the following and give the interval notation of the solution and show the solution on a number line. 6x-12(3-x) is less than or equal to 9(x-4)+9x

Solve the following and give the interval notation of the solution and show the solution-example-1

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4 votes

The Solution:

The given inequality is


6x-12(3-x)\leq9(x-4)+9x

Clearing the brackets, we get


6x-36+12x\leq9x-36+9x

Collecting the like terms, we get


\begin{gathered} 6x+12x-9x-9x\leq-36+36 \\ \end{gathered}
\begin{gathered} 18x-18x\leq0 \\ 0\leq0 \end{gathered}

So, the solution is true for all real values of x.

The interval notation of the solution is


(-\infty,\infty)

User Thor Jacobsen
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