Resources

🍰 Equations with fractions

Equations with denominators: we clear the fractions using the lowest common multiple and solve, with exact fractions and a check.

Equation

Write it with an = sign. Without =, it is taken as equal to 0. x², x^2, 0.5x, 3(x − 2) and fractions like x/2 all work.

Examples:

Solution

x = 4/3

y = (1/2)x + 1/3y = 1
xy−4−3−2−112345−3−2−11234Solution x = 4/3x = 4/3

Points

  • Solution:x = 4/3

Type

Linear

Solutions

1

Solving

  1. x/2 + 1/3 = 1
  2. Simplify each side (expand brackets and collect terms):
  3. (1/2)x + 1/3 = 1
  4. Move everything to the left and collect like terms:
  5. (1/2)x − 2/3 = 0
  6. (1/2)x = 2/3
  7. x = 2/3 / (1/2) = 4/3

Check

  1. Substitute each solution into both sides: they must match.
  2. With x = 4/3: left = 1, right = 1 ✓

On the graph

  1. Each side is a function: y = (1/2)x + 1/3 (blue) and y = 1 (pink). The solutions are the x values where the two graphs cross.

Practise

⚖️ Algebra Balance📝 Quadratics exam📝 Systems exam📈 Function problems🧰 More resources
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