Super Awesome Math

Solve for x Worksheets

One-step, two-step and x-on-both-sides equations · Grades 5–6

Linear equations to solve on paper, each with ruled space underneath for the working. Start with one step, such as x + 7 = 15 or 3x = 21, move to two steps with brackets and division, such as 2x − 5 = 11 or 3(x + 2) = 18, then to equations with x on both sides. Every equation is built backwards from its answer, so each step is a whole number and x is a positive integer up to 10, 20 or 100. The × and ÷ signs print as the language writes them.

Skills: solving equations, inverse operations, one-step and two-step equations, balancing both sides. Format: printable, randomized on every load.

Sheets are randomized, free to print, and carry no answer key on purpose – why Super Awesome Math works this way.

How to do it

Solving for x means getting x alone on one side, and every step does the same thing to both sides so that the two sides stay equal.

  1. Look at what has been done to x, then undo it in reverse order. In 3x + 7 = 22, x was multiplied then added to, so undo the addition first.
  2. Subtract 7 from both sides: 3x = 15. Whatever you do to one side you must do to the other, or the equation stops being true.
  3. Now undo the multiplication by dividing both sides by 3: x = 5.
  4. With x on both sides, first collect the x terms on one side by subtracting the smaller one from both: 5x − 2 = 3x + 8 becomes 2x − 2 = 8.
  5. Check by putting the answer back into the original equation. 3 × 5 + 7 = 22 is true, so x = 5 is right.

Where it goes wrong

  • Changing only one side. Subtracting 7 from the left and leaving the right alone breaks the balance the method depends on.
  • Undoing in the wrong order. Dividing 3x + 7 = 22 by 3 first gives x + 7/3, which is true but no simpler.

Frequently asked questions
What is the difference between a one-step and a two-step equation?
A one-step equation undoes a single operation: x + 7 = 15 is solved by taking 7 from both sides. A two-step equation has two operations wrapped around x, such as 2x − 5 = 11, and they are undone in reverse order, first adding 5 and then dividing by 2. Brackets and division by a number are two-step shapes too.
Why is there empty ruling under each equation?
Solving an equation is a sequence of steps, and each step belongs on its own line: what was done to both sides, then the new equation. The ruled rows give that working a place on the page, and there are more of them at the harder levels, where there are more steps to write.
Are the answers always whole numbers?
Yes. Every equation is built backwards from a whole-number answer between 1 and the chosen limit, so no step ever needs a fraction or a negative number. That keeps the attention on the method, undoing operations in the right order, rather than on the arithmetic.

Settings
  • Level: one step, two steps, or x on both sides
  • Answers: x up to 10, 20 or 100
  • Sign: × ÷ or · :
  • Columns: 2 or 3
  • Print an answer key

Example problems
  • x + 7 = 15
  • 3x = 21
  • 2x − 5 = 11
  • 5x − 3 = 2x + 9

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