Lesson 12~30 minUnit 2 · Patterns & Algebra+90 XP

Solving One-Step Equations (Add/Subtract)

Undo addition with subtraction and subtraction with addition, doing the same thing to both sides so the balance holds.

Today’s hook: $x + 7 = 12$. You can probably see the answer. The point of writing out the step is that $x + 4.83 = 12.19$ works exactly the same way, and that one you cannot see.

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Think First

warm-up

Before diving into the practice questions, take a moment to think about what you already know about this topic.

Record in workbook.

What You'll Master

objectives

Know

The inverse of addition is subtraction (and vice versa)

Understand

To solve an equation, undo the operation using its inverse, applied to both sides

Can Do

Solve equations of the form $x + a = b$
Solve equations of the form $x - a = b$

Words You Need

vocabulary

Inverse OperationAn operation that undoes another. Addition and subtraction are inverses of each other.

UndoTo reverse an operation. We undo $+5$ by doing $-5$, and undo $-3$ by doing $+3$.

BalanceBoth sides of an equation are equal, like a balanced scale. Any operation applied to one side must be applied to the other.

Additive InverseThe number you add to get zero. The additive inverse of $5$ is $-5$; of $-3$ is $+3$.

SolveTo find the value of the unknown that makes the equation true.

Inverse Operations

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Addition and subtraction are inverse operations they undo each other. This is the key to solving equations.

To isolate $x$, apply the inverse operation to both sides of the equation. Think of the equation as a balanced scale, whatever you do to one side, you must do to the other to keep it balanced.

$+5$ undone by $-5$

$x + 5 - 5 = x$. Adding then subtracting the same number gets you back to $x$.

$-3$ undone by $+3$

$x - 3 + 3 = x$. Subtracting then adding the same number returns to $x$.

The golden rule

Whatever is added to $x$, subtract it from both sides to isolate $x$.

Solving $x + a = b$

+5 XP

Method: subtract $a$ from both sides to isolate $x$.

When $x$ has something added to it, use subtraction to undo it. Apply the same subtraction to both sides to keep the equation balanced.

$x + a - a = b - a$

$x + 4 = 9$
Subtract 4 from both sides: $x + 4 - 4 = 9 - 4$
$x = 5$

$x + 7 = 15$
Subtract 7 from both sides: $x = 15 - 7 = 8$

$x + (-3) = 10$
Adding $-3$ is the same as subtracting 3. Add 3 to both sides: $x = 10 + 3 = 13$

Solving $x - a = b$

+5 XP

Method: add $a$ to both sides to isolate $x$.

When $x$ has something subtracted from it, use addition to undo it. Apply the same addition to both sides to keep the equation balanced.

$x - a + a = b + a$

$x - 3 = 7$
Add 3 to both sides: $x - 3 + 3 = 7 + 3$
$x = 10$

$x - 8 = 2$
Add 8 to both sides: $x = 2 + 8 = 10$

$x - 12 = -5$
Add 12 to both sides: $x = -5 + 12 = 7$

Watch Me Solve It · Worked examples

Watch Me Solve It · Two worked examples

+15 XP per step

Example A

PROBLEM

Solve $x + 6 = 14$

1

Identify the operation on $x$

$x$ has $+6$ added to it

The inverse of $+6$ is $-6$.
2

Subtract 6 from both sides

$x + 6 - 6 = 14 - 6$

Apply the inverse operation to both sides.
3

Simplify

$x = 8$

Left side: $x + 0 = x$. Right side: $14 - 6 = 8$.
4

Check your answer

$8 + 6 = 14$ ✓

Substitute $x = 8$ back in. Both sides equal 14.

Answer$x = 8$

Example B

PROBLEM

Solve $x - 9 = 3$

1

Identify the operation on $x$

$x$ has $9$ subtracted from it

The inverse of $-9$ is $+9$.
2

Add 9 to both sides

$x - 9 + 9 = 3 + 9$

Apply the inverse operation to both sides.
3

Simplify

$x = 12$

Left side: $x + 0 = x$. Right side: $3 + 9 = 12$.
4

Check your answer

$12 - 9 = 3$ ✓

Substitute $x = 12$ back in. Both sides equal 3.

Answer$x = 12$

Common Pitfalls

heads-up

Subtracting from one side only

Writing $x + 6 = 14 \Rightarrow x = 14$ (forgot to subtract 6 from the right side) breaks the balance. Both sides must stay equal.

Fix: always apply the inverse operation to both sides. $x + 6 - 6 = 14 - 6 \Rightarrow x = 8$.

Confusing the direction

Seeing $x + 6 = 14$ and adding 6 instead of subtracting it. If the equation shows $+6$, you subtract 6 from both sides, not add it.

Fix: ask "what is being done to $x$?" then do the opposite to both sides.

Forgetting to check

Skipping the verification step means a simple arithmetic slip can go unnoticed. Always substitute your answer back into the original equation.

Fix: for $x = 8$ from $x + 6 = 14$, check: $8 + 6 = 14$ ✓. If it doesn't balance, re-examine your working.

Quick Check · 5 questions

Solve $x + 9 = 14$.

+10 XP

Solve $x - 7 = 3$.

+10 XP

Solve $5 = x + 12$.

+10 XP

"A number increased by 6.5 equals 10." Which equation and solution are correct?

+10 XP

Which inverse operation solves $x - 2.8 = 5.4$?

+10 XP

Apply Easy 2 MARKS

Q1. Solve $x + 11 = 7$. Show your working and check your answer.

Answer in your workbook.

Apply Medium 3 MARKS

Q2. Solve $x - 3.6 = 8.9$. Show your working and check your answer.

Answer in your workbook.

Apply Hard 4 MARKS

Q3. A recipe needs 250g of flour. After adding some flour to a bowl, the chef adds another 75g and now has exactly 250g. Write an equation and solve to find how much flour was in the bowl to start with.

Answer in your workbook.

Stretch Challenge · +25 XP, +10 coins

One hidden number, two clues

One hidden number, two clues. Subtracting 7 from a hidden number gives $-3$. Adding 5 to the same number gives 9.

Write and solve a one-step equation for each clue. Do both clues identify the same number? Create a different one-step addition or subtraction equation with that solution, and check it.

Show your working first, then open the worked solution to check your reasoning.

Check the worked solution

The first clue gives $x-7=-3$, so add 7 to get $x=4$. The second gives $x+5=9$, so subtract 5 to get $x=4$. The clues agree. One possible new equation is $x-9=-5$; substituting 4 gives $4-9=-5$. Other equations are valid if substitution of 4 makes both sides equal.

Quick Review

Key Concept

Review the main ideas from this lesson.

Formulas

Key formulas and rules.

Watch Out

Common mistakes to avoid.

Check

Always verify your answers.

Practice

Keep practicing to master.

Build on these skills.

Interactive: Algebra Machine

Substitute numbers into algebraic expressions and see them evaluate step by step.

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← What is an Equation? Solving One-Step Equations (Multiply/Divide) →

Unit overview · Maths subject page · Unit quiz

Brain Trainer

⚡

Speed Drills, Solve These Equations!

Set a timer for 3 minutes. Solve as many as you can. Check your answers after.

$x + 5 = 13$

$x - 4 = 10$

$x + 7 = 2$

$x - 9 = -3$

$x + 2.5 = 8$

$6 = x + 9$

$x - 1.5 = 4.5$

$x + 12 = 5$

$-2 = x - 8$

$x + 0.75 = 2.25$

Solving One-Step Equations (Add/Subtract)

Printable Worksheets

Know

Understand

Can Do

One hidden number, two clues

Key Concept

Formulas

Watch Out

Check

Practice

Next

Interactive: Algebra Machine

Your Badges

Mark lesson as complete

Brain Trainer