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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 on a number line 6x123x is less than or equal to 9x49x class=

Respuesta :

The Solution:

The given inequality is

[tex]6x-12(3-x)\leq9(x-4)+9x[/tex]

Clearing the brackets, we get

[tex]6x-36+12x\leq9x-36+9x[/tex]

Collecting the like terms, we get

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

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

The interval notation of the solution is

[tex](-\infty,\infty)[/tex]

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