Foundation and Higher · inequalities

Inequalities on
a number line.
Open or closed?

and the one time
the sign flips

four symbols —

<  >  ≤  ≥

the wide end faces the bigger side

the extra line means or equal to

step 1 of 5

Greater than

1. Greater than 2: 2 itself is not included.

2. Open circle at 2, arrow to the right.

✓ x could be 2.1, 3, 50 …

step 2 of 5

Less than or equal to

1. ≤ means less than or equal to.

2. Closed circle: −1 is included.

✓ Extra line on the symbol, filled circle

step 3 of 5

Between two values

1. Closed at −2, open at 3. Join them.

2. Integers that fit: −2, −1, 0, 1, 2.

✓ 3 is not included

step 4 of 5

Solve like an equation

1. Do the same to both sides.

2. Keep the inequality sign throughout.

✓ Never swap it for =

2x + 3 < 11

2x < 8 − 3

x < 4 ÷ 2

step 5 of 5

The one trap

1. × or ÷ by a negative: flip the sign.

2. Check with an easy value like 0.

✓ Adding or subtracting never flips it

−2x < 6

x > −3 ÷ −2: flip the sign

check x = 0:  0 < 6 ✓

inequalities —

< and >

open circle: not included

≤ and ≥

closed circle: included

× or ÷ by a negative

flip the sign

Solve it like an equation,
but keep the inequality sign.

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