# How do you translate "8 times a number, x, decreased by y" into a algebraic expression?

Jan 3, 2016

$8 \cdot x - y$

#### Explanation:

Let me divide the dialogue in two parts
$\left(i\right)$ 8 times a number x.
$\left(i i\right)$decreased by y.

$\left(i\right)$
"8 times" means "8 multiplies by", "a number x" means "the number with which 8 is being multiplied is x".

Therefore, "8 times a number x" means "8 multiplied by x"
$8 \cdot x$

(ii)
"decreased" means "minus", "by y" means "y"
Therefore, "decreased by y" means "$- y$"

Therefore, the whole sentence represents $8 \cdot x - y$.