Undo the addition or subtraction
Remove the constant term from the side with x by applying the inverse operation to both sides.
1
Subtract 3 from both sides
Before
After
Answer
Interval
Set notation
Number line
Two Step Inequality Calculator
Solve any two-step inequality instantly — get step-by-step solutions, number line graphs, and interval notation. Free, no sign-up required.
two step inequality calculator with stepstwo step inequality calculator with graphtwo step inequality solver with number line
Why this page is built for two-step intent
Focused on the exact two-operation pattern students meet in Algebra 1: one addition or subtraction step, then one multiplication or division step.
Explains the sign-flip rule in the division step instead of skipping it — the most common source of wrong answers in two-step problems.
Pairs every answer with the full step sequence, a number-line graph, interval notation, and a verify tab so students can check their own work.
Two-Step Solver
Built for two-step inequalities: one add/subtract step followed by one multiply/divide step, with number line, interval notation, and sign-flip detection.
Live parse preview
2x + 3 > 7
Supported Input Styles
2x+3>7is the standard two-step form: subtract 3, then divide by 2.5x-4<=11adds 4 first, then divides by 5 — a positive divisor keeps the symbol.-3x+6>=0subtracts 6, then divides by -3 — the negative divisor flips the symbol.x/2+1<5subtracts 1, then multiplies by 2 — multiplication by a positive keeps the symbol.-2x-5>3adds 5, then divides by -2 — watch for the flip.
Math Keyboard
Tap symbols, numbers, or actions for fast linear-inequality input.
Result
The two-step solution isolates x > 2.
Solution2x+3 > 7
Interval(2, ∞)
1
Step 1
Step 1 — Undo the addition or subtraction
Remove the constant term from the side with x by applying the inverse operation to both sides.
Before
2x + 3 > 7
After
2x > 4
2
Step 2
Step 2 — Divide by the coefficient of x
Divide both sides by the number in front of x. If that number is positive, the symbol stays the same. If it is negative, the symbol flips direction.
Before
2x > 4
After
x > 2
3
Step 3
Step 3 — Check with a test value
Pick any number from inside the solution set and substitute it back into the original inequality to confirm the result.
Test x = 3: 2(3) + 3 = 9 > 7 ✓
Use the tabs to move between the algebra, graph, notation, and verification views.
Recent History
Saved locally in this browser so you can jump back into recent two-step problems without any backend.
Solve a few two-step inequalities and the latest ones will appear here.
Calculator Types
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How to Use the Two Step Inequality Calculator
The fastest way to use this calculator is to type the inequality exactly as it appears on your worksheet. You can enter forms such as 2x + 3 > 7, 5x - 4 <= 11, -3x + 6 >= 0, or x/2 + 1 < 5. The parser handles positive and negative coefficients, fractions, and all four inequality symbols without any special formatting.
After you enter a problem, the result area shows the isolated variable and the solution set. The Steps tab breaks the work into the two operations that define a two-step inequality: first the addition or subtraction that moves the constant, then the multiplication or division that removes the coefficient. The sign-flip rule is called out explicitly whenever you divide or multiply by a negative number, because that is the step where most Algebra 1 errors happen.
If you are checking homework, compare the Steps tab to your own work line by line. If you are learning the pattern for the first time, open the Graph tab after the Steps tab. Seeing x > 2 as a shaded ray on a number line makes the interval meaning concrete before you move on to the Interval Notation tab.
For a broader first-degree review, use the linear inequality calculator; for longer algebra chains, move next to the multi-step inequality calculator.
01
Enter a two-step inequality such as 2x + 3 > 7 or -3x + 6 >= 0.
02
Review the step cards to see the constant removed first, then the coefficient divided out, and whether the symbol flips.
03
Open the graph, interval notation, and verify tabs to confirm the answer from multiple angles.
What Is a Two-Step Inequality?
A two-step inequality is a one-variable inequality that requires exactly two operations to isolate the variable. The first operation removes an added or subtracted constant. The second operation removes a multiplied or divided coefficient. A typical example is 2x + 3 > 7, where subtracting 3 and then dividing by 2 leaves x > 2.
The two-step structure is the most common inequality pattern in Algebra 1 because it is the natural extension of two-step equations. The algebra moves are identical — combine constants, then isolate x — with one critical addition: if the second step divides or multiplies by a negative number, the inequality symbol must reverse direction.
Two-step inequalities always produce a single ray as the answer, not a bounded interval. The solution is either x > a, x < a, x >= a, or x <= a for some boundary value a. That boundary value is either included (closed circle, bracket notation) or excluded (open circle, parenthesis notation) depending on whether the original symbol was strict or inclusive.
Equation example
Inequality example
| Comparison point | Two-step equation | Two-step inequality |
|---|---|---|
| Goal | Find the exact value that makes both sides equal. | Find every value that keeps the comparison true. |
| Typical answer | A single value such as x = 2. | A ray such as x > 2 or x <= 5. |
| Sign flip rule | No flip — equality is symmetric. | Flip the symbol when dividing or multiplying by a negative. |
| Graph | One point on a number line. | A shaded ray with an open or closed endpoint. |
How to Solve Two-Step Inequalities Step by Step
The two-step process mirrors two-step equations almost exactly. The only rule that has no equation equivalent is the sign flip: whenever you divide or multiply both sides by a negative number, the inequality symbol reverses. Every other move — adding, subtracting, dividing by a positive — leaves the symbol unchanged. For a full rule review, see how to solve inequalities.
Step 1 — Remove the constant term
Identify the constant on the same side as the variable term. Add or subtract that value from both sides to leave the variable term alone. In 2x + 3 > 7, subtract 3 from both sides to get 2x > 4.
Example
Step 2 — Divide by the coefficient
Divide both sides by the number in front of x. If the coefficient is positive, the symbol stays the same. If the coefficient is negative, the symbol flips. In 2x > 4, dividing by 2 gives x > 2. In -3x > 6, dividing by -3 gives x < -2.
Example
The sign-flip rule
The sign flip applies only when you multiply or divide by a negative number. Adding or subtracting any number — positive or negative — never flips the symbol. A common mistake is flipping the symbol after subtracting a negative constant; that step does not trigger the rule.
Example
Only multiplication or division by a negative number reverses the inequality symbol.
Flipping after addition or subtraction
Adding or subtracting never reverses the inequality symbol, even if the number being added or subtracted is negative.
Forgetting the negative divisor
The sign flip happens when the coefficient of x is negative and you divide by it. Pause before the final step and check the coefficient.
Two Step Inequality Examples
The three cards below mirror the default problem: undo the constant, divide by the coefficient, and verify with a test value before moving to a new two-step inequality.
Divide by the coefficient of x
Divide both sides by the number in front of x. If that number is positive, the symbol stays the same. If it is negative, the symbol flips direction.
1
Divide both sides by 2
Before
After
Answer
Interval
Set notation
Number line
Check with a test value
Pick any number from inside the solution set and substitute it back into the original inequality to confirm the result.
1
Test x = 3
Before
After
Answer
Interval
Set notation
Number line
Two-Step Inequalities on a Number Line
A two-step inequality still graphs as one ray after x is isolated. For x > 2, mark 2 with an open endpoint and shade to the right because larger values satisfy the original comparison.
Inclusive symbols use closed endpoints, while strict symbols use open endpoints. This same endpoint choice carries into interval notation, so x > 2 becomes (2, infinity) and x >= 2 becomes [2, infinity).
Strict inequality
Use an open circle when the endpoint is excluded, as in x > 2 or x < -1.
Inclusive inequality
Use a closed circle when the endpoint is included, as in x >= 2 or x <= -1.
Interval Notation for Two-Step Inequalities
Interval notation is the compact form of the ray you get from a two-step inequality. Parentheses exclude the boundary, brackets include it, and infinity always uses a parenthesis.
After the two operations isolate x, translate the final symbol directly: x > 2 becomes (2, infinity), while x <= 5 becomes (-infinity, 5].
The full interval notation guide explains the bracket and parenthesis rules in more detail.
| Inequality | Interval notation | Number line | Meaning |
|---|---|---|---|
| Values greater than a, but not including a. | |||
| Values greater than a, including a. | |||
| Values less than a, but not including a. | |||
| Values less than a, including a. |
Frequently Asked Questions
What makes an inequality "two-step"?
It requires exactly two operations to isolate the variable — typically one addition or subtraction followed by one multiplication or division.
When does the inequality sign flip?
Only when you multiply or divide both sides by a negative number. Adding or subtracting any value never flips the symbol.
Can a two-step inequality have a fraction coefficient?
Yes. x/2 + 1 < 5 is a two-step inequality. Subtract 1 first, then multiply both sides by 2. Multiplying by a positive 2 keeps the symbol.
What does the answer look like on a number line?
A two-step inequality always produces a single ray — a shaded line extending left or right from one endpoint. The endpoint is open (hollow circle) for strict symbols and closed (filled circle) for inclusive symbols.
How is a two-step inequality different from a multi-step inequality?
A two-step inequality needs exactly two operations. A multi-step inequality may require distributing parentheses, combining like terms, or moving variable terms across the equals sign before the two-step pattern begins.
Does this calculator handle negative coefficients?
Yes. Enter -3x + 6 >= 0 or -2x - 5 > 3 and the calculator will apply the sign-flip rule automatically and label the step where it happens.
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Related Articles
Keep the same algebra rule set close by while you practice two-step problems, interval notation, and symbol meaning.