Solving Simple Equations

• Understand what an equation is: two expressions linked by an equals sign (=), true for specific value(s) of the variable.
• Identify the LHS (left-hand side) and RHS (right-hand side) of an equation.
• Find the solution (value of the unknown) by performing the same operation on both sides.
• Verify a solution by substituting back into the original equation.

Level 1 — Core idea

1. Equation vs expression

   • Expression: 3x + 5 (no equals sign; no fixed value until x is known).
   • Equation: 3x + 5 = 14 (states two expressions are equal; we solve for x).

2. Solution of an equation — The value of the variable that makes LHS = RHS.
   Example: x = 3 is a solution of x + 7 = 10 because 3 + 7 = 10.

3. Balanced equation rule (golden rule) — Whatever you do to one side, you must do to the other to keep the equation balanced.

   • Add the same number to both sides.
   • Subtract the same number from both sides.
   • Multiply both sides by the same non-zero number.
   • Divide both sides by the same non-zero number.

Level 2 — Process and representation

1. Solving one-step equations

   • x + a = b → subtract a from both sides: x = b − a.
   • x − a = b → add a to both sides: x = b + a.
   • ax = b → divide both sides by a: x = b/a.
   • x/a = b → multiply both sides by a: x = ab.

2. Solving two-step equations — Undo operations in reverse order (often undo addition/subtraction first, then multiplication/division).
   Example: 2x + 3 = 11 → 2x = 8 → x = 4.

3. Verification — Substitute the found value into the original equation. If LHS = RHS, the solution is correct.

Solve: x − 9 = 15

Step 1 — add 9 to both sides to isolate x:
         x − 9 + 9 = 15 + 9
Step 2 — simplify: x = 24
Verify: 24 − 9 = 15 ✓
Answer: x = 24

Solve: 3n + 4 = 19

Step 1 — subtract 4 from both sides: 3n = 15
Step 2 — divide both sides by 3: n = 5
Verify: 3(5) + 4 = 15 + 4 = 19 ✓
Answer: n = 5

• Solve y + 12 = 20. (y = 8)
• Solve 5m = 35. (m = 7)
• Solve 2p − 3 = 11. (p = 7)
• Verify whether x = 4 satisfies 3x − 5 = 7. (3×4 − 5 = 7 ✓)

Open the Practice tab for graded questions on solving simple equations.