How to Solve Two-Step Equations

What Is a Two-Step Equation?

A two-step equation is an equation that requires exactly two inverse operations to isolate the variable. Something like \(3x + 5 = 20\) — the variable \(x\) has been multiplied by 3 and then had 5 added to it. To get \(x\) by itself, you undo those two operations in reverse order.

The golden rule of equation solving: whatever you do to one side, you must do to the other. Every step keeps the equation balanced.

The Process: Always Undo in Reverse Order

Think of a two-step equation like putting on socks and shoes. You put socks on first, then shoes. To undo it, you take shoes off first, then socks — reverse order. Same idea here.

Step 1

Undo addition or subtraction first. Add or subtract the constant from both sides to get the term with the variable alone on one side.

Step 2

Undo multiplication or division second. Divide or multiply both sides by the coefficient to get the variable completely by itself.

Step 3

Check your answer. Plug it back into the original equation and confirm both sides are equal. This catches sign errors and arithmetic mistakes before they cost you points.

Worked Examples

Example 1 — Basic

Solve: \(3x + 5 = 20\)

Step 1 — Subtract 5 from both sides.
\(3x + 5 - 5 = 20 - 5\)
\(3x = 15\)

Step 2 — Divide both sides by 3.
\(x = 5\)

Check: \(3(5) + 5 = 15 + 5 = 20\) ✓

Example 2 — With Negatives

Solve: \(-4x + 7 = -13\)

Step 1 — Subtract 7 from both sides.
\(-4x = -20\)

Step 2 — Divide both sides by −4.
\(x = 5\)

Check: \(-4(5) + 7 = -20 + 7 = -13\) ✓

Example 3 — Variable on Right Side

Solve: \(14 = 2 + 3x\)

Step 1 — Subtract 2 from both sides.
\(12 = 3x\)

Step 2 — Divide both sides by 3.
\(x = 4\)

Check: \(2 + 3(4) = 2 + 12 = 14\) ✓
The variable being on the right side doesn't change anything — the process is identical.

Example 4 — Fraction Answer

Solve: \(5x - 3 = 9\)

Step 1 — Add 3 to both sides.
\(5x = 12\)

Step 2 — Divide both sides by 5.
\(x = \dfrac{12}{5}\)

This is a perfectly correct answer. Leave it as a fraction unless the problem asks for a decimal.

Common Mistakes to Avoid

Dividing before adding/subtracting. The most common one. In \(3x + 5 = 20\), students divide by 3 first and get \(x + 5 = \frac{20}{3}\). That's much messier and usually leads to a wrong answer. Always handle addition and subtraction first.

Forgetting to divide a negative coefficient. In \(-4x = -20\), dividing by \(-4\) gives positive \(5\), not negative. A negative divided by a negative is always positive.

Only doing the operation to one side. Whatever you do to the left side of the equation, you must do to the right side too. Both sides always stay balanced.

Skipping the check. Plugging your answer back in takes 20 seconds and catches almost every arithmetic error. Do it every time until it's automatic.

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