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Worksheets /Algebra and pre-algebra

One step equations worksheets

Equations solved in a single move — add, subtract, multiply or divide — with whole-number solutions by construction, so no answer ever comes out as a fraction.

Grade 5–Grade 8 · every refresh draws a new set · answer key included

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One step equations worksheets

Solve each equation.

1.
x + 10 = 11x =
2.
x + 3 = 4x =
3.
x + 7 = 14x =
4.
x + 4 = 12x =
5.
x + 5 = 8x =
6.
x ÷ 6 = 4x =
7.
x ÷ 2 = 6x =
8.
x ÷ 11 = 5x =
9.
2x = 18x =
10.
11x = 110x =
11.
11x = 44x =
12.
x + 9 = 21x =
13.
x − 4 = 2x =
14.
x + 11 = 15x =
15.
x ÷ 9 = 7x =
16.
x ÷ 12 = 10x =
17.
x − 1 = 2x =
18.
x ÷ 5 = 6x =
19.
12x = 144x =
20.
x − 4 = 0x =
Sheetsmith · sheetsmith.online · set afxw9pSheet 1 of 2

One step equations worksheets — answer key

Solve each equation.

1.
x + 10 = 11x = 1
2.
x + 3 = 4x = 1
3.
x + 7 = 14x = 7
4.
x + 4 = 12x = 8
5.
x + 5 = 8x = 3
6.
x ÷ 6 = 4x = 24
7.
x ÷ 2 = 6x = 12
8.
x ÷ 11 = 5x = 55
9.
2x = 18x = 9
10.
11x = 110x = 10
11.
11x = 44x = 4
12.
x + 9 = 21x = 12
13.
x − 4 = 2x = 6
14.
x + 11 = 15x = 4
15.
x ÷ 9 = 7x = 63
16.
x ÷ 12 = 10x = 120
17.
x − 1 = 2x = 3
18.
x ÷ 5 = 6x = 30
19.
12x = 144x = 12
20.
x − 4 = 0x = 4
Sheetsmith · sheetsmith.online · set afxw9pSheet 2 of 2

20 problems · US Letter · answer key — 2 sheets, page breaks marked in the preview

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What this worksheet is for

A one step equation asks for one move: whatever is being done to the letter, undo it. That sounds trivial and is the moment a lot of pupils quietly lose algebra, because they solve by inspection — reading the answer off the page — and never learn the method that later equations require. Every equation on this page is built from its own solution, so the answer is always a whole number and the practice stays on the method rather than on awkward arithmetic.

Who it suits

Grade 5 to Grade 8, ages ten to fourteen. Addition and subtraction equations come first, usually in Grade 5 or 6; multiplication and division follow. Negative numbers belong once integers have been taught, which is Grade 7 in most curricula.

How to use the settings

Keep the largest solution small at first — the size of the numbers is not the skill being practised, and a page of two-digit answers hides whether the pupil is using inverse operations or guessing. Turn on negatives only after integers are secure; the equation x + 8 = 3 is a different lesson from x + 3 = 8. Working space is worth adding here even though the arithmetic is short, because writing the inverse operation under both sides is the habit that makes two step equations possible.

What goes wrong

The commonest fault is applying the inverse to one side only, which produces an answer that satisfies nothing. The second is subtracting when the equation needs division: pupils read 4x = 12 as four plus x. Both are invisible on a page a pupil solves by inspection, which is the argument for larger numbers once the method is understood — inspection stops working and the method has to take over.

Questions

Are all the answers whole numbers?
Yes. Each equation is built backwards from a whole-number solution, so nothing comes out as a fraction. Fractional solutions are a separate topic and would make this page a poor place to learn the method.
What does “one step” mean?
One inverse operation solves it: add to both sides, subtract from both sides, multiply or divide both sides. Two step equations need two of those and have their own page.
Can I use a letter other than x?
Yes — the letter is a setting. It is worth changing occasionally, because pupils who only ever see x sometimes treat it as part of the notation rather than as a stand-in for a number.

Related worksheets

  • Two step equations worksheetsGrade 6–Grade 9
  • Order of operations worksheetsGrade 4–Grade 8
  • Integers worksheetsGrade 6–Grade 9

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