Grade 9 Algebraic Equations

Grade 9 equations: solving linear equations, equations with brackets and fractions, simple exponential equations and x² = k, plus word problems, with…

An equation says two expressions are equal, and solving it means finding the value of the variable that makes it true. In Grade 9 you solve equations with brackets, fractions and variables on both sides, simple exponential equations like 2ˣ = 16, and equations such as x² = 64.

You also turn word problems into equations. The method is always the same: do the same thing to both sides until the variable is on its own, then check your answer by substituting it back.

Key concepts

  • Inverse operations: undo addition with subtraction, multiplication with division
  • Equations with brackets and variables on both sides
  • Equations with fractions: multiply by the lowest common denominator
  • Simple exponential equations, e.g. 3ˣ = 81
  • Equations of the form x² = k have two solutions
  • Writing an equation from a word problem

Worked examples

Solve: 2(x − 3) = x + 4

Expand: 2x − 6 = x + 4. Subtract x from both sides: x − 6 = 4. Add 6: x = 10. Check: 2(7) = 14 and 10 + 4 = 14 ✓.

Solve: x² = 64

Both 8² and (−8)² equal 64, so x = 8 or x = −8.

Solve: x/3 + 2 = x/2

Multiply every term by 6: 2x + 12 = 3x. Subtract 2x: x = 12. Check: 4 + 2 = 6 and 12/2 = 6 ✓.

The sum of three consecutive numbers is 72. Find the numbers.

Let the numbers be x, x + 1 and x + 2. Then 3x + 3 = 72, so 3x = 69 and x = 23. The numbers are 23, 24 and 25.

Solve: 3ˣ = 81

Write 81 as a power of 3: 3 × 3 × 3 × 3 = 81, so 81 = 3⁴. The bases are equal, so x = 4.

Common mistakes

  • Doing something to only one side of the equation.
  • Multiplying only some of the terms by the common denominator.
  • Giving only x = 8 for x² = 64.
  • Not checking the answer in the original equation.

Exam tips

  • Write each step on a new line with the equals signs lined up.
  • In word problems, write 'Let x = …' so the marker knows what x means.
  • Substitute your answer back in to check before moving on.

Frequently asked questions

What is the difference between an expression and an equation?

An expression has no equals sign (2x + 3); you simplify it. An equation has an equals sign (2x + 3 = 11); you solve it.

How do I solve 2ˣ = 16?

Write 16 as a power of 2: 16 = 2⁴. The bases are equal, so x = 4.

Do Grade 9 learners solve quadratic equations?

Only simple ones like x² = k. Solving quadratics by factorising is Grade 10 work.

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