I am trying to help my daughter with her algebra. She has the following problem;
$$|3x-6| \leq 5 - 2x $$
I can solve it for the two possible answers, but then she needs to graph the answer and put the answer in interval notation form. Can anyone help me? The answers I get are $x \leq \frac{11}{5}$, or $x \leq 1$.
On
The inequality $|3x-6| \leq 5-2x$ means $ 2x-5 \leq 3x-6 \leq 5-2x$. The first inequality gives $x\geq 1$. The second gives $x \leq \frac{11}{5}$, so this matches your response. In interval notation, this would be written as $[1,\frac{11}{5}]$. You can see what the graph would look like by plotting it on the number line. I have done this for you here https://www.wolframalpha.com/input/?i=1%5Cleq+x+%5Cleq+11%2F5
If we have that $a\leq x\leq b$, the interval notation for that is
$$[a,b]$$