Algebra 2 · Unit 1A · Lesson 1

One-step equations

Keep the equation balanced. Use inverse operations to get the variable alone—and explain why each step works.

Video lesson11 worked examples4 printable PDFs

01 / THE GOAL

By the end, you can…

Solve addition, subtraction, multiplication, and division equations.
Use reciprocals when the coefficient is a fraction.
Name the property of equality and check the solution in the original equation.

Before you start: Signed-number arithmetic, order of operations, and adding and multiplying fractions.

02 / WATCH & LEARN

A little guidance goes a long way.

Keep your notes nearby. Pause whenever you need to try a step yourself.

One-step addition and subtraction equationsKhan Academy · Lesson video

Khan AcademyGuest lesson · Shawn Todd’s video will replace this when available.

Watch on YouTube ↗

One-step multiplication and division with fractions and decimalsKhan Academy · Lesson video

Khan AcademyGuest lesson · Shawn Todd’s video will replace this when available.

Watch on YouTube ↗

03 / THE MAIN IDEA

Let’s make it click.

An equation is a balance.

The two sides represent the same value. Keep them equal by doing the same operation to both sides. The goal is to write the variable by itself.

x+4=9 \quad\Longrightarrow\quad x+4-4=9-4

Subtracting 4 from both sides is the Subtraction Property of Equality.

Undo the operation, not the number.

Addition and subtraction undo each other. Multiplication and division undo each other. Ask what is being done to the variable, then apply the inverse operation to both sides.

x+a=b\Rightarrow x=b-a \qquad ax=b\Rightarrow x=\frac{b}{a}\ (a\ne0)

Division by zero is never allowed. For a fractional coefficient, multiply by its reciprocal.

Write the property. Then check.

Use the Addition, Subtraction, Multiplication, or Division Property of Equality to justify your step. If your result is written with the variable on the right, use the Symmetric Property to switch sides. Substitute the solution into the original equation to check.

5=x\quad\Longleftrightarrow\quad x=5

04 / SEE THE STEPS

One step. Then the next.

These examples follow the problem types on your practice sheet. Use Next step to reveal the reasoning, or open the complete solution to read at your own pace.

PRACTICE 1, 6, 11

Undo addition

Solve x + 4 = 9 and state the property used.

x+4=9

The variable has 4 added to it. Undo addition by subtracting 4.

Step 1 of 3

Read the complete solution

$x+4=9$
The variable has 4 added to it. Undo addition by subtracting 4.
$x+4\color{#176b58}{-4}=9\color{#176b58}{-4}$
Subtract 4 from both sides: Subtraction Property of Equality.
$\boxed{x=5}$
Check: 5 + 4 = 9. Both sides are 9.

PRACTICE 2, 5

Undo subtraction

Solve x − 3 = 6.

x-3=6

Subtracting 3 is undone by adding 3.

Step 1 of 3

Read the complete solution

$x-3=6$
Subtracting 3 is undone by adding 3.
$x-3\color{#176b58}{+3}=6\color{#176b58}{+3}$
Add 3 to both sides: Addition Property of Equality.
$\boxed{x=9}$
Check: 9 − 3 = 6.

PRACTICE 3, 22

Undo multiplication

Solve 6x = 18.

6x=18

6x means 6 multiplied by x. Undo multiplication with division.

Step 1 of 3

Read the complete solution

$6x=18$
6x means 6 multiplied by x. Undo multiplication with division.
$\frac{6x}{\color{#176b58}{6}}=\frac{18}{\color{#176b58}{6}}$
Divide both sides by 6: Division Property of Equality.
$\boxed{x=3}$
Check: 6(3) = 18.

PRACTICE 4, 12, 16

Undo division

Solve x/3 = 5.

\frac{x}{3}=5

The variable is divided by 3. Multiply by 3 to undo it.

Step 1 of 3

Read the complete solution

$\frac{x}{3}=5$
The variable is divided by 3. Multiply by 3 to undo it.
$\color{#176b58}{3}\left(\frac{x}{3}\right)=\color{#176b58}{3}(5)$
Multiply both sides by 3: Multiplication Property of Equality.
$\boxed{x=15}$
Check: 15 ÷ 3 = 5.

PRACTICE 7–10, 24

The variable can be on either side

Solve 8 = x/2. Give the answer as x = a number.

8=\frac{x}{2}

The location of the variable does not change the inverse operation.

Step 1 of 3

Read the complete solution

$8=\frac{x}{2}$
The location of the variable does not change the inverse operation.
$2(8)=2\left(\frac{x}{2}\right)\ \Rightarrow\ 16=x$
Multiply both sides by 2: Multiplication Property of Equality.
$\boxed{x=16}$
Switch sides using the Symmetric Property. Check: 8 = 16/2.

PRACTICE 13, 14, 17

Add or subtract a fraction

Solve x − 1/2 = 1/4.

x-\frac12=\frac14

Undo subtraction by adding 1/2 to both sides.

Step 1 of 3

Read the complete solution

$x-\frac12=\frac14$
Undo subtraction by adding 1/2 to both sides.
$x-\frac12+\frac12=\frac14+\frac12$
Addition Property of Equality. Use a common denominator on the right.
$x=\frac14+\frac24=\boxed{\frac34}$
Check: 3/4 − 1/2 = 3/4 − 2/4 = 1/4.

PRACTICE 15, 18, 23

Use a reciprocal

Solve (2/5)x = 6.

\frac25x=6

The coefficient 2/5 multiplies x. Its reciprocal is 5/2.

Step 1 of 3

Read the complete solution

$\frac25x=6$
The coefficient 2/5 multiplies x. Its reciprocal is 5/2.
$\frac52\cdot\frac25x=\frac52\cdot6$
Multiply both sides by 5/2: Multiplication Property of Equality.
$x=\frac{30}{2}=\boxed{15}$
The reciprocal makes the coefficient 1. Check: (2/5)(15) = 6.

PRACTICE 19–20

Review: evaluate a numerical expression

Evaluate 2 · 3² − 5(6 − 4).

2\cdot3^2-5(6-4)

Start with grouping and exponents.

Step 1 of 3

Read the complete solution

$2\cdot3^2-5(6-4)$
Start with grouping and exponents.
$2\cdot9-5(2)=18-10$
Calculate the power and parentheses, then multiply.
$\boxed{8}$
Subtract last. A fraction bar is also grouping: evaluate its numerator before dividing.

PRACTICE 21

Review: substitute into a formula

Find P = nRT/V for n = 0.65, R = 0.08, T = 293, and V = 14.

P=\frac{nRT}{V}

Replace each letter with its given value. Keep the whole numerator grouped.

Step 1 of 3

Read the complete solution

$P=\frac{nRT}{V}$
Replace each letter with its given value. Keep the whole numerator grouped.
$P=\frac{(0.65)(0.08)(293)}{14}=\frac{15.236}{14}$
Multiply the numerator before dividing by the denominator.
$P\approx\boxed{1.09}$
Round at the end. The numerical result is about 1.09 in the units implied by the supplied constants.

PRACTICE 25

Review: a formula with units

A tire has a radius of 13 inches. How far does it travel in one revolution?

C=2\pi r

One full revolution covers one circumference.

Step 1 of 3

Read the complete solution

$C=2\pi r$
One full revolution covers one circumference.
$C=2\pi(13)=26\pi\text{ inches}$
Substitute the radius. Keep π until the final calculation.
$C\approx\boxed{81.7\text{ inches}}$
Round to one decimal place and include units.

PRACTICE 26–27

Review: distribute and combine like terms

Simplify −3(2x − 4) + 5x − 2.

-3(2x-4)+5x-2

Multiply every term inside the parentheses by −3.

Step 1 of 3

Read the complete solution

$-3(2x-4)+5x-2$
Multiply every term inside the parentheses by −3.
$-6x+12+5x-2$
A negative times a negative is positive. This is the Distributive Property.
$(-6x+5x)+(12-2)=\boxed{-x+10}$
Combine variable terms with variable terms and constants with constants. This is an expression to simplify, not an equation to solve.

05 / NOTES & PRACTICE

Your lesson toolkit.

Open a PDF in a new tab to read or print it, or download a copy for your device.

NOTES · PDF · 2 PAGES

Blank notes

Follow along and show each property of equality.

Open PDF ↗Download ↓

WORKED NOTES · PDF · 2 PAGES

Completed notes

The annotated classroom notes, with worked solutions.

Open PDF ↗Download ↓

TRY IT YOURSELF · PDF · 2 PAGES

Practice

27 problems: equations, fractions, and prerequisite review.

Open PDF ↗Download ↓

ANSWER SHEET · PDF · 2 PAGES

Completed practice

The scanned classroom answer sheet. Show your work first, then compare.

Open PDF ↗Download ↓

06 / CHECK YOURSELF

Give it a try.

Your turn: solve −4 = x + 7. Which property do you use?Think it through, then tap to reveal the answer.

$\boxed{x=-11}$

Subtract 7 from both sides: Subtraction Property of Equality. This gives −11 = x. Use the Symmetric Property to write x = −11. Check: −11 + 7 = −4.

← Back to Algebra 2 Get the lesson materials ↑