Understanding Compound Inequalities

'Or' requires only one condition to be true, 'and' requires both.

'Or' and 'and' both require both conditions to be true.

'Or' and 'and' both require only one condition to be true.

'Or' requires both conditions to be true, 'and' requires only one.

Addition

Subtraction

Multiplication

Division

Y < 11

Y > 11

Y > 5

Y < 5

It becomes an equal sign.

It remains the same.

It becomes a greater than sign.

It flips direction.

X < -2

X > 2

X > -2

X < 2

Only one inequality must be true.

Both inequalities must be true.

Neither inequality must be true.

At least one inequality must be false.

X ≤ 5

X ≤ 17

X ≥ 5

X ≥ 17

Add 7 to both sides.

Subtract 7 from both sides.

Divide both sides by 3.

Multiply both sides by 3.

M ≥ -3

M ≤ 3

M ≥ 3

M ≤ -3

M is greater than or equal to -3 and less than 2.

M is less than or equal to -3 and greater than 2.

M is greater than or equal to 2 and less than -3.

M is less than or equal to 2 and greater than -3.