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Generate Simple Equations Worksheets

Learn to solve basic one-step and two-step linear equations involving variables.

Finding the Unknown: Simple Equations

Simple equations are mathematical statements where two expressions are equal, containing one unknown variable to solve for. By performing the same operation on both sides β€” adding, subtracting, multiplying, or dividing β€” students isolate the variable and find its value. This balance principle is the cornerstone of all algebraic problem-solving.

Components of Simple Equations

This section covers the techniques for solving one-step and two-step equations:

  • One-Step Equations: Equations requiring a single inverse operation to isolate the variable (e.g., x + 5 = 12).
  • Two-Step Equations: Equations requiring two operations in the correct order β€” typically undo addition/subtraction first, then multiplication/division.
  • Checking Solutions: Substituting the answer back into the original equation to verify both sides are equal.
  • Word Problems to Equations: Translating real-world scenarios into equations and solving them.

Examples of Simple Equations

One-Step Equation Examples

  • Solve x + 8 = 15: Subtract 8 from both sides to get x = 15 - 8 = 7.
  • Solve 3n = 27: Divide both sides by 3 to get n = 27 Γ· 3 = 9.
  • Solve y - 12 = 5: Add 12 to both sides to get y = 5 + 12 = 17.

Two-Step Equation Examples

  • Solve 2x + 3 = 11: First subtract 3 from both sides to get 2x = 8, then divide by 2 to get x = 4.
  • Solve 5n - 7 = 18: First add 7 to both sides to get 5n = 25, then divide by 5 to get n = 5.
  • Solve x/4 + 2 = 6: First subtract 2 to get x/4 = 4, then multiply by 4 to get x = 16.

Checking Solutions Examples

  • For x + 8 = 15 with x = 7: Check 7 + 8 = 15 βœ“.
  • For 2x + 3 = 11 with x = 4: Check 2(4) + 3 = 8 + 3 = 11 βœ“.
  • For 5n - 7 = 18 with n = 5: Check 5(5) - 7 = 25 - 7 = 18 βœ“.

Word Problem Examples

  • A number plus 9 equals 22. Write x + 9 = 22, subtract 9 from both sides, x = 13.
  • Three times a number minus 4 equals 20. Write 3n - 4 = 20, add 4 to get 3n = 24, divide by 3 to get n = 8.
  • A taxi charges $3 plus $2 per mile, and the fare is $15. Write 2m + 3 = 15, subtract 3 to get 2m = 12, divide by 2 to get m = 6 miles.