Algebra Practice

One-Step Linear Equations Practice Test

Solve one-step equations with integers, fractions, decimals, negative coefficients, and simple applications.

One-Step Linear Equations Practice Test

20 one-step equation questions with worked solutions and incorrect-choice analysis.

Instant feedback · Worked explanations
After the test · inverse operation station

A one-step equation asks one question: which single operation will undo what is attached to the variable?

These equations are short, but they train one of algebra’s most important habits: recognizing inverse operations. Addition is undone by subtraction, multiplication by division, and division by multiplication. The equation stays valid because the same operation is applied to both sides.

AdditionSubtractionMultiplicationDivision Negative numbersFractionsDecimalsQuick checks
Inverse-operation pairs

Every basic one-step equation belongs to one of four inverse pairs

+ ↔ −x + 7 = 19
subtract 7
− ↔ +x − 6 = 11
add 6
× ↔ ÷5x = 35
divide by 5
÷ ↔ ×x/4 = 8
multiply by 4
Equation snapshots

Read the operation first, then choose the inverse

Additive equation x + 9 = 14
Subtract 9 → x = 5
Multiplicative equation 6x = 42
Divide by 6 → x = 7
Subtraction equation x − 13 = −4
Add 13 → x = 9
Division equation x/5 = 7
Multiply by 5 → x = 35
Signed-number checkpoint

A negative coefficient changes the arithmetic, not the solving rule

−4x = 28
x = 28 ÷ (−4)
x = −7

The variable is multiplied by −4, so divide both sides by −4. Treat the sign as part of the coefficient.

Before accepting the answer, check its sign mentally: a negative coefficient times a negative solution gives a positive result.
Reciprocal lane

A fractional coefficient can be undone by multiplying by its reciprocal

For (3/5)x = 12, multiply both sides by 5/3.

Equation(3/5)x = 12
Inverse operation× 5/3 on both sides
Solutionx = 20
Decimal coefficient lane

Decimals still use the same inverse operation

Equation0.4x = 6
Undo ×0.4x = 6 ÷ 0.4
Solutionx = 15

If decimal division feels awkward, rewrite 0.4 as 2/5 and multiply by 5/2.

Simple proportion

A proportion can often collapse to a one-step multiplication or division

Startx/6 = 5/3
→
Multiply by 6x = 10

Because x is already divided by 6, multiplying both sides by 6 isolates it directly.

One-step models

Short real-world equations work the same way once the unknown quantity is identified

Repeated cost 5 identical tickets cost $60.
5t = 60
t = $12
Distance A runner covers d miles in 4 equal laps.
d/4 = 3
d = 12 miles
Temperature change The final value is 7 more than x.
x + 7 = 18
x = 11
7x = 63
↓
“What number times 7 gives 63?”
↓
x = 9
Mental reasonableness check

One-step equations are simple enough to estimate before you finish the arithmetic

A quick mental check catches many sign and operation errors immediately.

If 8x = 40, x should be smaller than 40.
If x/5 = 12, x should be larger than 12.
If x + 20 = 13, x must be negative.
If −3x = 18, x must be negative.
One-step error radar

Most wrong answers come from choosing the wrong inverse or losing a sign

x + 8 = 20 → x = 28 x = 12

Undo +8 with subtraction, not addition.

−5x = 30 → x = 6 x = −6

Dividing a positive number by a negative coefficient gives a negative result.

x/7 = 4 → x = 4/7 x = 28

Undo division by 7 with multiplication by 7.

(2/3)x = 10 → x = 20/3 x = 15

Multiply by the reciprocal 3/2, not by 2/3 again.

Use the score diagnostically

A missed one-step equation usually identifies one very specific weakness

That makes this topic useful for diagnosing foundational algebra before moving to multi-step equations.

Inverse choiceThe wrong opposite operation was selected.
Signed arithmeticThe algebra was right, but a negative sign was lost.
Fractions & decimalsReciprocals or coefficient division caused the error.
CheckingThe result was not tested in the original equation or context.