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Grade 10 Algebra Expressions Equations — How to Identify the Question Type

Grade 10 algebra questions split into two distinct tasks: simplifying an expression (no x to find) or solving an equation (find x). Reading the instruction word tells you which one before you start.

Type 1: Simplifying an algebraic expression

Trigger words: "Simplify", "Expand and simplify", "Factorise"

Trigger structure: No equals sign — or an equals sign with no variable to find. The question asks you to change the form, not find a value.

Do not confuse with: Solving — if the question says 'solve for x', you must find a numeric answer, not just rewrite the expression.

Method (no numbers — just the steps)

  1. Identify the operation: expanding brackets, factorising, or simplifying a fraction
  2. Expand any brackets first (FOIL or distribution)
  3. Collect like terms
  4. Factorise if instructed — look for common factor, difference of squares, or trinomial
Grade 10Paper 1Level 1 — Knowledge
1.1 Simplify: (2x − 3)(x + 5) − 2(x² + x − 1)

Source: DBE Mathematics Paper 1, November 2019, Question 1.1

Common mistake

Incorrectly expanding (a + b)² as a² + b² — the middle term 2ab is missing.

See the progression — same type, increasing difficulty

Easy
Simplify: 3x(x − 4) + x²

Practice question — not sourced from a past paper.

Medium
Simplify: (x + 3)(x − 3) − (x − 1)²

Practice question — not sourced from a past paper.

Hard
Factorise fully: 2x³ − 8x

Practice question — not sourced from a past paper.

Type 2: Solving a linear equation

Trigger words: "Solve for x", "Find x"

Trigger structure: One equation, x appears to the first power only (no x² or higher).

Do not confuse with: Solving a quadratic — if there is an x², the method changes completely.

Method (no numbers — just the steps)

  1. Clear any fractions by multiplying through by the LCD
  2. Expand brackets
  3. Move all x-terms to one side, constants to the other
  4. Divide both sides by the coefficient of x
Grade 10Paper 1Level 1 — Knowledge
Solve for x: 3(x − 2) = x + 4

Practice question — not sourced from a past paper.

See the progression — same type, increasing difficulty

Easy
Solve for x: 2x + 5 = 11

Practice question — not sourced from a past paper.

Medium
Solve for x: (x + 1)/2 − (x − 3)/3 = 1

Practice question — not sourced from a past paper.

Hard
Solve for x: 2(3x − 1) − 3(x + 2) = x − 8

Practice question — not sourced from a past paper.

Type 3: Solving a quadratic equation

Trigger words: "Solve for x", "Find the roots"

Trigger structure: x² is present and the question says 'solve'.

Do not confuse with: Simplifying — if there is no instruction to solve or find x, you may only need to factorise without solving.

Method (no numbers — just the steps)

  1. Rearrange so the equation equals zero: ax² + bx + c = 0
  2. Factorise (common factor, trinomial, or difference of squares)
  3. Set each factor equal to zero
  4. Solve each resulting linear equation
Grade 10Paper 1Level 2 — Routine Procedures
2.1 Solve for x: x² − x − 6 = 0

Source: DBE Mathematics Paper 1, November 2021, Question 2.1

Common mistake

Dividing both sides by x to cancel it — this loses the solution x = 0.

See the progression — same type, increasing difficulty

Easy
Solve for x: x² − 9 = 0

Practice question — not sourced from a past paper.

Medium
Solve for x: 2x² + 5x = 3

Practice question — not sourced from a past paper.

Hard
Solve for x: 3x(x + 2) = x + 10

Practice question — not sourced from a past paper.

Type 4: Solving a linear inequality

Trigger words: "Solve for x", "For which values of x"

Trigger structure: An inequality sign (< > ≤ ≥) appears instead of an equals sign.

Do not confuse with: An equation — the critical difference is that multiplying or dividing by a negative number flips the inequality sign.

Method (no numbers — just the steps)

  1. Solve as you would a linear equation
  2. If you multiply or divide by a negative number, reverse the inequality sign
  3. Write the answer as an inequality or on a number line if asked
Grade 10Paper 1Level 2 — Routine Procedures
Solve for x: −2x + 3 > 7

Practice question — not sourced from a past paper.

Common mistake

Forgetting to reverse the inequality sign when dividing by a negative coefficient.

See the progression — same type, increasing difficulty

Easy
Solve for x: 3x − 4 < 8

Practice question — not sourced from a past paper.

Medium
Solve for x: 1 − 2x ≥ 5

Practice question — not sourced from a past paper.

Hard
Solve for x and represent the solution on a number line: 3(x − 1) ≤ 2(x + 1) − (x + 4)

Practice question — not sourced from a past paper.

Words like determine and hence appear throughout this topic — see the instruction word glossary for full definitions.