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🔣 Equations with brackets

Equations with brackets: we use the distributive property to remove them, then isolate x, step by step and with 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 = 5

y = 3x − 6y = x + 4
xy−2−11234567−10−551015Solution x = 5x = 5

Points

  • Solution:x = 5

Type

Linear

Solutions

1

Solving

  1. 3(x − 2) = x + 4
  2. Simplify each side (expand brackets and collect terms):
  3. 3x − 6 = x + 4
  4. Move everything to the left and collect like terms:
  5. 2x − 10 = 0
  6. 2x = 10
  7. x = 10 / 2 = 5

Check

  1. Substitute each solution into both sides: they must match.
  2. With x = 5: left = 9, right = 9 ✓

On the graph

  1. Each side is a function: y = 3x − 6 (blue) and y = x + 4 (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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