Maths Maestri

What this quiz covers

Grade 8 Algebraic Equations Quiz 5 draws its questions at random from 32 questions across these topics:

Worked examples

A few of the question types, with full solutions, so you know what to expect.

Two-step equations. Solve for \(x\): \(x - 6 = 2\)

  1. \(x = 8\)
  2. \(x = -4\)
  3. \(x = 4\)
  4. \(x = -8\)

Answer: \(x = 8\)

Undo the \(-6\) by adding 6 to BOTH sides.

\(x = 2 + 6\)

Two-step equations. Solve for \(x\): \(5x = 20\)

  1. \(x = 4\)
  2. \(x = 15\)
  3. \(x = 25\)
  4. \(x = 100\)

Answer: \(x = 4\)

\(5x\) means 5 TIMES \(x\), so divide both sides by 5.

Tip: Subtracting 5 would give 15 - that is the classic error here.

Two-step equations. Solve for \(x\): \(3x + 7 = 12\)

  1. \(x = \dfrac{5}{3}\)
  2. \(x = 5\)
  3. \(x = \dfrac{19}{3}\)
  4. \(x = 2\)

Answer: \(x = \dfrac{5}{3}\)

Undo the \(+7\) first: \(3x = 12 - 7 = 5\).

Now divide both sides by 3.

Tip: A fraction answer is completely correct. Do not force a whole number.

Two-step equations. Solve for \(x\): \(2x + 9 = 3\)

  1. \(x = -3\)
  2. \(x = 3\)
  3. \(x = 6\)
  4. \(x = -6\)

Answer: \(x = -3\)

\(2x = 3 - 9 = -6\)

Divide both sides by 2.

Two-step equations. Solve for \(x\): \(4x - 5 - x = 10\)

  1. \(x = 5\)
  2. \(x = 3\)
  3. \(x = 15\)
  4. \(x = \dfrac{5}{3}\)

Answer: \(x = 5\)

Collect the \(x\) terms first: \(4x - x = 3x\).

\(3x - 5 = 10\), so \(3x = 15\).

Tip: Tidy each side BEFORE moving anything across.