SAT — mathFoundational7 min read

Solving One-Step and Two-Step Equations

Master one-step and two-step equations for the Digital SAT. Learn inverse operations with clear worked examples and practice problems.

Tutor AI Team2026-02-25T01:07:10.179Z

Solving equations is the single most fundamental skill tested on the Digital SAT Math section. At its core, solving an equation means finding the value of the variable that makes both sides equal. One-step and two-step equations are the simplest forms, but they appear frequently — often embedded inside more complex problems.

If you can solve these quickly and accurately, you build a foundation for every other algebra topic on the test: systems of equations, inequalities, function evaluation, and even some geometry problems that require setting up an equation first.

In this guide, you will learn the inverse-operation method for one-step equations, extend it to two-step equations, and practise on SAT-style problems.

Core Concepts

What Is an Equation?

An equation is a mathematical statement that two expressions are equal. For example:

$3x + 5 = 20$

The variable $x$ represents an unknown value. Your job is to isolate $x$ — get it by itself on one side of the equation.

Inverse Operations

Every operation has an inverse (opposite) that undoes it:

Operation	Inverse
Addition ( $+$ )	Subtraction ( $-$ )
Subtraction ( $-$ )	Addition ( $+$ )
Multiplication ( $\times$ )	Division ( $\div$ )
Division ( $\div$ )	Multiplication ( $\times$ )

The golden rule: whatever you do to one side of the equation, you must do to the other side.

One-Step Equations

A one-step equation requires exactly one inverse operation to solve.

Addition/Subtraction type:

$x + 9 = 14$

Subtract 9 from both sides:

$x = 14 - 9 = 5$

Multiplication/Division type:

$5x = 35$

Divide both sides by 5:

$x = \frac{35}{5} = 7$

Division type:

$\frac{x}{4} = 6$

Multiply both sides by 4:

$x = 6 \times 4 = 24$

Two-Step Equations

A two-step equation requires two inverse operations. The standard approach is:

Undo addition or subtraction first (deal with the constant term).
Undo multiplication or division second (deal with the coefficient).

Example: Solve $3x + 7 = 22$

Step 1 — Subtract 7 from both sides: $3x = 15$

Step 2 — Divide both sides by 3: $x = 5$

Example: Solve $\frac{x}{2} - 3 = 10$

Step 1 — Add 3 to both sides: $\frac{x}{2} = 13$

Step 2 — Multiply both sides by 2: $x = 26$

Equations with Negative Coefficients

When the coefficient of $x$ is negative, divide by the negative number at the end.

Example: Solve $-4x + 9 = 1$

Subtract 9: $-4x = -8$

Divide by $-4$ : $x = 2$

Fractional and Decimal Answers

SAT equations don't always have neat integer answers. Be comfortable with fractions and decimals.

Example: Solve $5x + 2 = 11$

$5x = 9$

$x = \frac{9}{5} = 1.8$

Checking Your Answer

Substitute your answer back into the original equation to verify:

For $3x + 7 = 22$ with $x = 5$ : LHS $= 3(5) + 7 = 22$ ✓

Strategy Tips

Tip 1: Work Backwards Through the Order of Operations

When solving, you reverse PEMDAS. The last operation performed on $x$ in the expression is the first one you undo.

Tip 2: Keep Track of Negative Signs

Many errors on the SAT come from sign mistakes. Write each step carefully, especially when subtracting negatives.

Tip 3: Use Mental Math for Simple Equations

On the SAT, time matters. If you see $x + 3 = 10$ , you should instantly know $x = 7$ without writing steps. Save your detailed work for harder problems.

Tip 4: Watch for Equations Disguised in Word Problems

The SAT often presents one-step or two-step equations inside word problems. The key is translating English into algebra. "A number increased by 5 equals 12" becomes $x + 5 = 12$ .

Tip 5: Validate with Answer Choices

On multiple-choice questions, you can substitute each answer choice back into the equation. This is especially useful when you're unsure of your algebra.

Worked Example: One-Step

Problem

If $x - 8 = 15$ , what is the value of $x$ ?

Add 8 to both sides:

$x = 15 + 8 = 23$

Solution

Worked Example: Two-Step

Problem

If $4x - 3 = 29$ , what is the value of $x$ ?

Add 3: $4x = 32$

Divide by 4: $x = 8$

Check: $4(8) - 3 = 32 - 3 = 29$ ✓

Solution

Worked Example: SAT-Style Context

Problem

A gym charges a $25 registration fee plus$ 15 per month. If Marco has paid a total of $115, how many months has he been a member?

Let $m$ = number of months.

$15m + 25 = 115$

Subtract 25: $15m = 90$

Divide by 15: $m = 6$

Marco has been a member for 6 months.

Solution

Worked Example: Fraction Coefficient

Problem

Solve $\frac{2x}{3} + 5 = 11$

Subtract 5: $\frac{2x}{3} = 6$

Multiply by 3: $2x = 18$

Divide by 2: $x = 9$

Solution

Worked Example: Negative Result

Problem

Solve $7x + 4 = -10$

Subtract 4: $7x = -14$

Divide by 7: $x = -2$

Check: $7(-2) + 4 = -14 + 4 = -10$ ✓

Solution

Practice Problems

Problem 1

Solve $x + 14 = 31$ .

Problem 2

Solve $6x = -42$ .

Problem 3

Solve $3x - 8 = 19$ .

Problem 4

Solve $\frac{x}{5} + 7 = 10$ .

Problem 5

A streaming service charges $9 per month plus a one-time activation fee of$ 12. If the total cost after several months is $66, how many months of service were purchased?

Problem 6

Solve $-2x + 11 = 3$ .

Want to check your answers and get step-by-step solutions?

Common Mistakes

Performing an operation on only one side. If you add 5 to the left, you must add 5 to the right too. This is the most basic but most critical rule.
Sign errors with negatives. When you subtract a negative, you get a positive: $-(-3) = +3$ . Watch this carefully.
Undoing operations in the wrong order. In two-step equations, undo addition/subtraction before multiplication/division. Doing it backwards leads to errors.
Forgetting to check. Substituting back takes seconds and catches arithmetic mistakes.
Misreading the question. Some SAT questions ask for $2x + 1$ rather than $x$ . Always read what the question actually asks for.

Frequently Asked Questions

How do I know if I should add or subtract first?

Look at what's happening to the variable. In $3x + 7 = 22$ , the $x$ is being multiplied by 3 and then 7 is added. Undo in reverse order: subtract 7 first, then divide by 3.

What if the variable is on the right side?

It doesn't matter. $15 = x + 8$ is the same as $x + 8 = 15$ . Solve the same way: $x = 7$ .

Are one-step equations really on the SAT?

Yes, though usually embedded in context (word problems) or as part of a larger problem. The SAT adaptive format includes simpler questions in the first module.

Should I show my work on the SAT?

The SAT doesn't grade your work, only your answer. But writing steps in your test booklet helps avoid careless errors, especially under time pressure.

What if my answer is a fraction — should I convert to a decimal?

The SAT accepts both forms. For student-produced response questions, enter the fraction as-is or convert to a decimal. Either is fine.

Key Takeaways

✓
One-step equations need a single inverse operation to isolate $x$ .
✓
Two-step equations require two operations: undo addition/subtraction first, then multiplication/division.
✓
Golden rule: whatever you do to one side, do to the other.
✓
Always check by substituting back into the original equation.
✓
Read carefully — the SAT may ask for an expression like $3x - 1$ rather than just $x$ .
✓
Speed matters — practise until simple equations are automatic mental math.

Tags:

#sat#math#algebra#equations#foundational

Ready to Ace Your SAT math?

Get instant step-by-step solutions to any problem. Snap a photo and learn with Tutor AI — your personal exam prep companion.

Core Concepts

What Is an Equation?

Inverse Operations

One-Step Equations

Two-Step Equations

Equations with Negative Coefficients

Fractional and Decimal Answers

Checking Your Answer

Strategy Tips

Tip 1: Work Backwards Through the Order of Operations

Tip 2: Keep Track of Negative Signs

Tip 3: Use Mental Math for Simple Equations

Tip 4: Watch for Equations Disguised in Word Problems

Tip 5: Validate with Answer Choices

Worked Example: One-Step

Worked Example: Two-Step

Worked Example: SAT-Style Context

Worked Example: Fraction Coefficient

Worked Example: Negative Result

Practice Problems

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Common Mistakes

Frequently Asked Questions

Key Takeaways

Related Topics

Parallel Structure

Verb Tense and Consistency

Modifier Placement and Dangling Modifiers

Ready to Ace Your SAT math?