Translating expressions equations, & inequalities

Question

Four times the difference of a number and 7 is 32

Answer 1

Hi Ally,

Here, you are essentially being asked to translate English to Algebra. Let’s break this down.

“Four times the difference between a number and 7

You know 4 comes first, you know difference implies subtracting two numbers—you can express a number as x or n—I’ll use n:

4 (n - 7)

”is 32”

The word is always implies an equals sign in problems like these, so:

4( n - 7) = 32

You were not asked to solve the equation, so I would consider that your final answer,

Answer 2

Let "x" be the unknown number.

The "difference of the number and 7" (i.e., the distance between the number and 7) is |x - 7|, where the pair of vertical bars is the "absolute value" symbol.

So

4 · |x - 7| = 32,

where the dot is the multiplication symbol.

Divide both sides by 4 to get

|x - 7| = 8

Therefore x is 8 away from 7.

Therefore x is either 15 or -1.