Which operation do I undo first?

Addition or subtraction first, multiplication or division second — the reverse of the usual order of operations, because you are unwrapping the equation from the outside in.

What if the variable term is negative?

Solve exactly the same way, then divide by the negative coefficient at the end. Dividing an equation by a negative does not flip the equals sign — that rule only applies to inequalities.

What if the answer is not a whole number?

Fractions and decimals are perfectly valid solutions: 4x + 1 = 8 gives x = \frac{7}{4}. Check it by substituting back, same as always.

How are two-step equations different from one-step equations?

One extra layer: a one-step equation has a single operation to undo, a two-step has two (a constant to clear and a coefficient to divide away). The balance rule — same move on both sides — is identical.

Can Photo Math Solver show the check step too?

Yes — solutions end by substituting the answer back into the original equation, the same verification your teacher wants to see on paper.

You can start solving two-step equations for free by adding the Chrome extension — try it on your own worksheet before deciding if you need anything more.

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Photo Math Solver Solved

2x + 3 = 11

1Subtract $3$ from both sides: $2x = 8$ .
2Divide both sides by $2$ : $x = 4$ .
3Check: $2(4) + 3 = 11$ ✓.

On this page01Summary 02Definition 03Formulas 04Methods 05Examples 06Practice 07Mistakes 08FAQ

Summary

A two-step equation is solved by undoing addition or subtraction first and multiplication or division second — the reverse of the order you would use to evaluate it.

Strip the constant off the variable side, divide through by the coefficient, and check by substituting the result back into the original equation.

This works while the variable appears exactly once; brackets to expand or a variable on both sides make it a linear equation, where terms have to be collected before any undoing starts.

01Definition

What is a two-step equation?

A two-step equation puts two operations on the variable at once — usually a multiplication or division paired with an addition or subtraction, like $4x - 5 = 19$ . Solving it means undoing both, one at a time.

The order matters, and it runs in reverse: the equation was built by first multiplying $x$ by 4, then subtracting 5 — so you unwrap it backwards, adding 5 first, dividing by 4 second. Think of unwrapping a present: last layer on, first layer off.

Master this pattern and you have the core move of all of algebra: every longer equation — with parentheses, fractions, or variables on both sides — eventually simplifies down to exactly this two-step finish.

Where you'll actually use this

Phone plans: "$25 base fee plus $10 per gigabyte came to $65" is $10x + 25 = 65$ .
Taxi and delivery pricing: a fixed pickup fee plus a per-mile rate is the classic $ax + b = c$ .
Saving up: "I have $40 and save $15 a week — when do I reach $130?" is $15x + 40 = 130$ .
Temperature conversion: solving $F = \frac{9}{5}C + 32$ for $C$ is a two-step equation.

02Formulas

The formulas you need

Keep these on hand — every method below builds on them.

Standard form

ax + b = c

A coefficient on x plus a constant — the shape every two-step equation reduces to.

The solution

x = \frac{c - b}{a}

Move the constant first (subtract b), then divide by the coefficient a.

Order of undoing

\pm \text{ first}, \quad \times\div \text{ second}

Reverse of the order of operations — undo the outermost layer (addition/subtraction) first.

Fraction form

\frac{x}{a} + b = c \;\Rightarrow\; x = a(c - b)

Same order: clear the constant first, then multiply through by the divisor.

03Methods

How to solve two-step equations

Pick the method that fits the problem in front of you.

When to use it: The classic

ax + b = c

shape, like

2x + 3 = 11

— a coefficient on the variable and a constant to clear.

1Undo the addition or subtraction first: subtract $3$ from both sides, giving $2x = 8$ .
2Undo the multiplication: divide both sides by $2$ , giving $x = 4$ .
3Check: $2(4) + 3 = 11$ ✓.

04Worked examples

Two-Step Equations, solved step by step

From easy to hard — pick a problem to see its full solution.

2x + 3 = 11

1Subtract $3$ from both sides: $2x = 8$ .
2Divide both sides by $2$ : $x = 4$ .
3Check: $2(4) + 3 = 11$ ✓.

Try it on your own two-step equations homework

Photo Math Solver reads a two-step equation straight from a screenshot — worksheet, textbook, or online quiz — and shows both moves in the right order: constants first, coefficient second, each applied to both sides, with a check at the end. No retyping decimals or negatives, and no second-guessing which step comes first.

05Practice

Now you try

Work each one on paper first, then check your answer.

Problem 1

3x + 4 = 19

Problem 2

\frac{x}{2} - 5 = 1

Problem 3

6x - 7 = 29

Problem 4

-4x + 9 = 1

Stuck on your two-step equations homework? Screenshot it

Two-step equations with decimals or negative coefficients are easy to mistype into a calculator. Screenshot the equation with Photo Math Solver wherever it appears — homework PDF, textbook page, online quiz — and get the isolated-variable steps without re-entering the numbers.

06Common mistakes

Where points get lost

Each of these shows up on real graded work — and each has a simple fix.

The mistake	Why it happens	The fix
Dividing before moving the constant: turning $2x + 3 = 11$ into $x + 3 = 5.5$ .	Dividing by the coefficient feels like the most direct route to $x$ , so it gets done first.	Undo in reverse order of operations: clear the added or subtracted constant first, divide last. (If you must divide first, you have to divide every term — usually messier.)
Applying a step to only one side.	After the first step succeeds, attention shifts to the variable side and the other side gets left behind.	Write each operation under both sides before simplifying — every line of working should keep the scale balanced.
Dropping the sign when dividing by a negative coefficient.	From $-3x = -6$ , dividing by $3$ instead of $-3$ feels close enough but flips the answer’s sign.	Divide by the coefficient exactly as written, sign included: $\frac{-6}{-3} = 2$ . Then substitute back to confirm.
In $5 - 2x = 17$ , subtracting the $2x$ instead of the $5$ .	The constant appearing first in reading order makes the variable term look like the thing to remove.	Rewrite the left side as $-2x + 5$ first. Now it is a standard two-step: subtract $5$ , then divide by $-2$ .

Photo Math Solver shows every intermediate step, so slips like these are easy to catch before they cost you marks.

07FAQ