How many linear inequality questions does the SAT ask?

Usually 1 to 3 across the two adaptive modules. They belong to the Algebra domain, which is about 35 percent of the math section, and they appear at every difficulty.

When do I flip the inequality sign?

Only when you multiply or divide both sides by a negative number. Adding, subtracting, or dividing by a positive leaves the direction alone.

What does at least mean in an inequality?

At least 50 translates to greater than or equal to 50. At most 50 translates to less than or equal to 50. The boundary value counts in both, which is exactly what strict inequalities refuse.

Can Desmos shade inequalities?

Yes. Type y ≤ 2x + 3 and the solution region shades itself instantly. It is the fastest check available for questions asking which point satisfies an inequality.

Why do these drills keep changing their numbers?

Each one is a generator. A fresh version forces you to redo the reasoning about direction and boundaries instead of recognizing an answer you met last week.

Algebra · Skill 4 of 5

SAT Linear Inequalities Practice

Inequality questions on the digital SAT are algebra with a judgment call attached: which way does the sign point, and does the boundary count? Below are the recurring setups, one complete walkthrough, the classic sign flip traps, and free drills that regenerate endlessly.

Domain: Algebra
About 35% of the test is Algebra
Difficulty: easy to hard
Free, no account

Drill inequalities now → Every Algebra skill

The patterns behind every version

Inequality questions rotate through a short list of costumes. Here is the whole wardrobe.

Pattern 01

Solve, watching the flip

These solve exactly like equations until you multiply or divide by a negative number, which reverses the sign. From −3x + 7 < 22 you reach −3x < 15, and dividing by −3 gives x > −5.

Pattern 02

Translate the phrase

At least becomes ≥, at most becomes ≤, and more than stays strict. Often the entire question is whether you can turn a sentence about a budget or a weight limit into the right symbol.

Pattern 03

Which point works

You get something like y > 2x + 1 and a handful of candidate points. Substitute each pair and keep what makes the statement true, remembering that points sitting on a strict boundary fail.

Pattern 04

Real constraints, rounded right

A word problem fixes a minimum revenue or a maximum capacity, you solve, and the boundary lands between whole numbers. The context then decides whether the answer rounds up or down.

Watch one solved completely

Worked example · medium

A freelance designer charges $60 per hour and pays a $90 software subscription out of each week's earnings. She wants to clear at least $1,500 this week after paying the subscription. What is the least whole number of hours she must bill?

Earnings after the subscription are 60h − 90, so clearing at least $1,500 means 60h − 90 ≥ 1,500.
Add 90 to both sides: 60h ≥ 1,590.
Divide by 60: h ≥ 26.5. No sign flip, since 60 is positive.
Hours billed must be whole, and the goal is a minimum, so round up. At 27 hours she clears 60 × 27 − 90 = 1,620 − 90 = 1,530, which meets the target; at 26 hours she would clear only 1,560 − 90 = 1,470, which falls short.

Answer: 27 hours

Whether it is billable hours or banquet tables, the routine holds: translate the words, solve the inequality, then round in the direction the story demands.

Where students give points back

Flipping when you should not. Adding or subtracting never reverses an inequality. Students burned once by the flip rule start flipping everywhere, which is its own reliable way to miss.
Not flipping when you must. Dividing −4x > 20 by −4 gives x < −5. Miss that reversal and every check you run afterward happily confirms the wrong region.
Rounding against the story. When h ≥ 26.5 and hours must be whole, the answer is 27. When a maximum is involved, you round down instead. Direction comes from context, not habit.
Treating strict as inclusive. More than 40 excludes 40 itself. Answer choices love to park the boundary value right where a rushed reader will grab it.

Desmos on inequality questions

Type the inequality with its sign intact and Desmos shades every point that satisfies it. Asked whether (3, 7) works? Plot the point and see whether it lands inside the shaded region. Notice the boundary line too: Desmos draws it dashed when the inequality is strict, a visual reminder of whether the edge counts.

Why drilling here is different

You cannot memorize your way through drills that refuse to hold still. Satified's inequality generators reroll their rates, fees, and thresholds on every load, so the flip decision stays a real decision each time. Behind them sits a bank of 1,483 questions in which every answer and explanation has been verified.

Flip the sign, never the outcome.

Practice inequalities free →

Asked constantly, answered here

How many linear inequality questions does the SAT ask?: Usually 1 to 3 across the two adaptive modules. They belong to the Algebra domain, which is about 35 percent of the math section, and they appear at every difficulty.
When do I flip the inequality sign?: Only when you multiply or divide both sides by a negative number. Adding, subtracting, or dividing by a positive leaves the direction alone.
What does at least mean in an inequality?: At least 50 translates to greater than or equal to 50. At most 50 translates to less than or equal to 50. The boundary value counts in both, which is exactly what strict inequalities refuse.
Can Desmos shade inequalities?: Yes. Type y ≤ 2x + 3 and the solution region shades itself instantly. It is the fastest check available for questions asking which point satisfies an inequality.
Why do these drills keep changing their numbers?: Each one is a generator. A fresh version forces you to redo the reasoning about direction and boundaries instead of recognizing an answer you met last week.

Build outward

Inequalities borrow every move from equations and then add direction. Each of these skills sharpens the others.