How to Solve Multi-Step Equations? (+FREE Worksheet!)

Algebra 1

How to Solve Multi-Step Equations

A multi-step equation just means you’ll do a few moves — distribute, combine like terms, then undo addition and multiplication — before $x$ stands alone. Learn the order and these stop feeling scary. We’ll work plenty together, with a solver, drills, and a worksheet maker one tap away.

⚡ Step-by-Step Solver 📄 Worksheet Maker ✏️ Practice Drills 📇 Flashcards

Illustration of students learning How to Solve Multi-Step Equations

If a one-step equation is a single move, a multi-step equation is a short combo: maybe a parenthesis to distribute, some like terms to combine, variables on both sides to gather, and then the usual “undo” steps to free $x$. It looks busier, but every move is one you already know. The secret is doing them in a sensible order — and we’ll practice that order until it feels automatic. Every move here is one you already know from one-step equations; we’re just chaining a few together.

The big idea

What Is a Multi-Step Equation?

A multi-step equation is an equation that takes two or more operations to isolate the variable — for example $3(x-2)+4=16$. You solve it by simplifying each side first (distribute, then combine like terms), then gathering the variable on one side and undoing operations, all while keeping the equation balanced.

The reliable order of moves:

Distribute to clear any parentheses.
Combine like terms on each side.
Move the variables to one side (add/subtract).
Undo addition/subtraction, then multiplication/division.

Tutor tip: Think of it as “tidy up first, then unwrap.” Distributing and combining are the tidying; the last two steps are the unwrapping that gets $x$ by itself.

From Tangle to Solution, Step by Step

Here’s the order in action on $3(x – 2) + 4 = 16$:

Step 1

Distribute

$3(x-2)+4=16$
$\Rightarrow 3x-6+4=16$

Step 2

Combine

$3x-6+4=16$
$\Rightarrow 3x-2=16$

Step 3

Unwrap

$3x-2=16$
$\Rightarrow 3x=18\Rightarrow x=$ 6

Worked Examples

Tidy up, then unwrap — each card follows the equation down to its solution.

Example A — Variables on both sides

Solve $2x + 5 = 15 – x$.

Add $x$ to both sides: $3x + 5 = 15$.
Subtract 5: $3x = 10$.
Divide by 3: $x = \tfrac{10}{3}$ — a fraction is a fine answer.

Answer: $x = \tfrac{10}{3}$

Example B — Distribute first

Solve $3(x – 2) + 4 = 16$.

Distribute: $3x – 6 + 4 = 16$.
Combine: $3x – 2 = 16$; add 2: $3x = 18$.
Divide by 3: $x = 6$.

Answer: $x = 6$

Example C — Gather the variables

Solve $7x – 4 = 3x + 16$.

Subtract $3x$: $4x – 4 = 16$.
Add 4: $4x = 20$; divide: $x = 5$.
Check: $7(5)-4 = 31 = 3(5)+16$ ✓

Answer: $x = 5$

Example G — Clear the fraction first

Solve $\dfrac{x}{2} + 3 = 7$.

Multiply every term by 2: $x + 6 = 14$.
Subtract 6: $x = 8$.
Clearing the denominator early keeps the rest clean.

Answer: $x = 8$

Example D — No solution

Solve $2x + 1 = 2x + 5$.

Subtract $2x$: $1 = 5$.
The variable vanished and left a false statement.
So there’s no solution.

Answer: no solution

Example E — Infinitely many

Solve $3(x + 1) = 3x + 3$.

Distribute: $3x + 3 = 3x + 3$.
Both sides are identical — true for every $x$.
So there are infinitely many solutions.

Answer: infinitely many

Example F — A real-world setup

A taxi charges $3 plus $2 per mile. For a $17 ride: solve $2m + 3 = 17$.

Subtract 3: $2m = 14$.
Divide by 2: $m = 7$.
Name the unknown and the word problem becomes a multi-step equation.

Answer: 7 miles

Slip-Ups That Cost Easy Points

Distributing to only the first term. $3(x-2)$ is $3x – 6$, not $3x – 2$. Multiply the outside number by every term inside.
Forgetting to do it to both sides. Subtract 5 from the left? Subtract 5 from the right too. That’s what keeps the equation true.
Sign errors when moving terms. Moving $+3x$ across makes it $-3x$. Write the step out instead of doing it in your head.
Panicking at “no solution” or “all reals.” If the variable disappears, a false line ($1=5$) means no solution and a true line ($3=3$) means infinitely many. That’s information, not a mistake.

Your Turn: Solve These

Work each by hand, then reveal the answers. Stuck on one? The step-by-step solver shows every move.

$5x – 7 = 3x + 9$
$2(x – 4) = 10$
$6x + 4 = 2x – 12$
$-3(x – 5) = 9$
$\dfrac{x}{3} + 2 = 5$
$10 – 2x = 4x – 8$
$4x + 2 = 4x – 7$

Show answers

$\color{blue}{x=8}$
$\color{blue}{x=9}$
$\color{blue}{x=-4}$
$\color{blue}{x=2}$
$\color{blue}{x=9}$
$\color{blue}{x=3}$
$\color{blue}{\text{no solution } (2=-7\text{ is false})}$

Keep practicing

Make Your Own Equations Worksheet

Generate fresh multi-step equations with a full answer key — print or save as a PDF.

Unlimited problems, made instantly

Complete answer key included

📄 Open the Worksheet Maker ✏️ Quick Practice Drills

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Frequently Asked Questions

What’s the first thing I should do in a multi-step equation?

Tidy up before you unwrap: distribute to clear parentheses, then combine like terms on each side. Only after the equation is simplified do you move variables and undo operations.

Which side should I move the variables to?

Either works, but moving them to the side that keeps the $x$-coefficient positive avoids sign mistakes. For $2x = 5 – 3x$, adding $3x$ to both sides is cleaner than subtracting.

What does it mean when the variable disappears?

If you’re left with a false statement like $1 = 5$, there’s no solution. If you’re left with a true one like $4 = 4$, every number works (infinitely many solutions).

Do I always distribute before combining like terms?

Yes — clear parentheses first. If you try to combine terms before distributing, you’ll merge things that aren’t actually like terms yet. Distribute, then combine, then solve.

How do I check my answer?

Plug it back into the original equation and confirm both sides match. It takes ten seconds and catches almost every sign slip.

Continue Your Study

Ready for the next step? Pick up right where this lesson leaves off:

Up nextHow to Find the MidpointContinue with Expressions and EquationsOpen lesson →Up nextHow to Find the Distance Between Two PointsContinue with Expressions and EquationsOpen lesson →Up nextSimplifying Variable ExpressionsContinue with Expressions and EquationsOpen lesson →

Effortless Math Team

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Effortless Math Team

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