Question

Write the inequality as a sentence and solve it. ten minus a number is greater than or equal to 21.

Answer 1

'Ten minus a number' this translates as:

`10-x`

'is greater than or equal to 21'. This means that the expression above is > or = to 21:

`10-x\ge21`

To solve it we have to do the same operations in both sides of the inequality.

First we add x in both sides. This way, we'll get possitive x on the right side:

`\begin{gathered} 10-x+x\ge21+x \\ 10\ge21+x \end{gathered}`

And finally we substract 21 on both sides:

`\begin{gathered} 10-21\ge21+x-21 \\ 10-21\ge x \end{gathered}`

And finally we compute the substraction. The solution of the inequality is:

`-11\ge x`

That can also be writen as:

`x\leq-11`

Is the same expression written backwards, it's easier to read.