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

Question

asked Dec 28, 2023 179k views

1 Answer

Thor Jacobsen · Answer 1 · 2023-12-31T22:58:39+0000

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

$(-\infty,\infty)$