Are these Linear Inequalities notes free?

Yes. The full 3-page Linear Inequalities sheet is free inside CapCompass, which runs in your browser with no account needed.

What does the Linear Inequalities revision sheet cover?

The rules, and the one that bites, adding or subtracting keeps the sign, multiplying by a positive keeps it, multiplying by a negative FLIPS it, at least k, no less than k, at most k, no more than k, Four signs, and the words that hide them, greater than, at least, less than, at most, Equation vs Inequality.

Is this for Digital SAT SAT Math?

Yes, it is written for the Digital SAT SAT Math syllabus.

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Linear Inequalities — Digital SAT SAT Math revision notes

A 3-page visual revision sheet for Linear Inequalities, written for Digital SAT SAT Math. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.

Linear Inequalities revision notes, page 1 of 3 — A preview of page 1 — all 3 pages open full size in the app.

Linear Inequalities in one look

solve it like an equation, with one rule that can turn the whole thing around

The rules, and the one that bites

adding or subtracting keeps the sign a < b ⇒ a + c < b + c
multiplying by a positive keeps it a < b, k > 0 ⇒ ka < kb
multiplying by a negative FLIPS it a < b, k < 0 ⇒ ka > kb
at least k, no less than k x ≥ k
at most k, no more than k x ≤ k

Q. Solve 5 - 3x < 2x + 20.

gather the x terms on the left: 5 - 3x - 2x < 20
5 - 5x < 20, then subtract 5: -5x < 15
divide both sides by -5, and flip the sign because -5 is negative

Answer: x > -3

Four signs, and the words that hide them

greater than: more than, over, exceeds. The boundary is excluded
at least: no less than, minimum of, a floor. The boundary counts
less than: under, below, fewer than. The boundary is excluded
at most: no more than, maximum of, capacity, budget. The boundary counts

Equation vs Inequality

Equation

the answer is a single value of x
the graph of a two-variable one is a line
every legal move keeps the equals sign as it is

Inequality

the answer is a whole range of values
the graph of a two-variable one is a region on one side of a line
dividing by a negative reverses the sign

Page 1 of 3. The full sheet, all 3 pages, opens free in the app.

What this Linear Inequalities sheet covers

The rules, and the one that bites
adding or subtracting keeps the sign
multiplying by a positive keeps it
multiplying by a negative FLIPS it
at least k, no less than k
at most k, no more than k
Four signs, and the words that hide them
greater than
at least
less than
at most
Equation vs Inequality
Equation
Inequality
Turning a sentence into an inequality
What the picture is doing
Traps that cost points
Tricks that save time

Open the full Linear Inequalities sheet →Free, works offline, no account needed. All 3 pages, plus a study plan built around your own exam dates.

How CapCompass uses this sheet

These notes are not a standalone PDF. CapCompass plans SAT Math chapter by chapter against your real exam dates and free hours, and when the plan reaches Linear Inequalities the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.