# At a Glance - Inequalities

We have four possible inequality signs to choose from: <, >, ≤, and ≥. There's also the slightly less popular ^, which means that everything below is greater than everything above, but that brings us into a touchy area, spiritually speaking. Translating English into one of these symbols is a matter of common sense. Good thing you have some of that.

The signs < and > are usually straightforward.

• "Three is less than x'' can be abbreviated by 3 < x.

• "5 is more than x'' can be written in symbols as 5 > x.

When we're translating into statements that use ≤ or ≥, we have a slightly wider range of English phrases to use. For example, each of the following English statements translates into symbols as x ≤ 20.

• x is less than or equal to twenty.

• x is at most twenty.

• x is not more than twenty.

• x is not greater than twenty.

• Twenty could be more than x, or it could be exactly as much as x. You'll never know. Na-nana-boo-boo.

Each of these following English statements translates into symbols as x ≥ 0.

• x is greater than or equal to zero.

• x is not less than zero.

• x is not smaller than zero.

• x is at least zero.

#### Exercise 1

Translate the English sentence into a mathematical equation or inequality as appropriate:

Three y plus seven equals forty-two.

#### Exercise 2

Translate the English sentence into a mathematical equation or inequality as appropriate:

Seven-eighths of x is at most thirty.

#### Exercise 3

Translate the English sentence into a mathematical equation or inequality as appropriate:

Nine is less than y.

#### Exercise 4

Translate the English sentence into a mathematical equation or inequality as appropriate:

Three less than one-fifth of y is eleven.

#### Exercise 5

Translate the English sentence into a mathematical equation or inequality as appropriate:

z minus one is at least negative two.

#### Exercise 6

Translate the English sentence into a mathematical equation or inequality as appropriate:

#### Exercise 7

Translate the English sentence into a mathematical equation or inequality as appropriate:

The ratio of x and four is greater than the difference of x and two.

#### Exercise 8

Translate the English sentence into a mathematical equation or inequality as appropriate:

The total of x and five is no more than four.

#### Exercise 9

Translate the English sentence into a mathematical equation or inequality as appropriate:

Three times z yields fifty-one.

#### Exercise 10

Translate the English sentence into a mathematical equation or inequality as appropriate:

x combined with the difference of x and four yields three.