OpenStudy (gibby):

The sum of a number and 2 is no less than the product of 9 and the same number.

OpenStudy (wholock):

This is a numerical inequality in algebraic form, so we just need to translate it.

OpenStudy (gibby):

ok

OpenStudy (mathstudent55):

The best way to translate a sentence into an equation is to do a piece at a time.

OpenStudy (wholock):

So it goes x + 2 = <-- (the sum of a number and 2) No less means is can be equal to and greater than, so x + 2 >/= and then the product of 9 and the same number: x + 2 >/= 9 * x

OpenStudy (mathstudent55):

\(\small\bf The ~sum ~of \color{red}{~a ~number} ~and ~2 ~is ~no ~less ~than ~the ~product ~of ~9 ~and ~the ~same ~number.\) "A number" stands for an unknown number, so we use a variable to represent the unknown number. A variable is a letter, usually small case. "x" is very popular. \(\small\bf The ~sum ~of \color{red}{~a ~number} ~and ~2 ~is ~no ~less ~than ~the ~product ~of ~9 ~and ~the ~same ~number.\) \(\small \bf~~~~~~~~~~~~~~~~~~~~~~~~~~~~\color{red}{x} \)

OpenStudy (mathstudent55):

A sum is an addition. You need to add 2 to the unknown number. \(\small\bf \color{green}{The ~sum ~of \color{red}{~a ~number} ~and ~2} ~is ~no ~less ~than ~the ~product ~of ~9 ~and ~the ~same ~number.\) \(\small \bf~~~~~~~~~~~~~~~~~~~~~~~~~~~~\color{red}{x}~~~~\color{green}{+~~~2} \)

OpenStudy (mathstudent55):

A product means a multiplication. \(\small\bf \color{green}{The ~sum ~of \color{red}{~a ~number} ~and ~2} ~is ~no ~less ~than \color{blue}{~the ~product ~of ~9 ~and ~the \color{red}{~same ~number}.}\) \(\small \bf~~~~~~~~~~~~~~~~~~~~~~~~~~~~\color{red}{x}~~~~\color{green}{+~~~2}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\color{blue}{9}\color{red}{x} \)

OpenStudy (mathstudent55):

"is no less" means that the number can be equal or it can be greater. It just cannot be less. \(\small\bf \color{green}{The ~sum ~of \color{red}{~a ~number} ~and ~2} \color{purple}{~is ~no ~less ~than} \color{blue}{~the ~product ~of ~9 ~and ~the \color{red}{~same ~number}.}\) \(\small \bf~~~~~~~~~~~~~~~~~~~~~~~~~~~~\color{red}{x}~~~~\color{green}{+~~~2}~~~~~~~~~~~\color{purple}{\ge}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\color{blue}{9}\color{red}{x} \) Now you get rid of all the colors and extra spacing, and you have: \(\large x + 2 \ge 9x\)

OpenStudy (wholock):

Dang, that's way better than I put it for sure! I see why you are Honorary Professor!

OpenStudy (gibby):

thank you!

OpenStudy (mathstudent55):

@Wholock You gave a great explanation, but be careful with terms. You wrote "No less means is can be equal to and greater than, so" You need "or" instead of "and". It should read "No less means is can be equal to or greater than, so"

OpenStudy (wholock):

Thanks for the tip, I try to be a little careful when it comes to word usage, but I slip up a lot...

OpenStudy (mathstudent55):

I missed something else. "No less means **it** can be equal to or greater than, so"