Question

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

Answer 1

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)`