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How to Solve a Bracket?

Published in Math Operations 2 mins read

Solving a bracket, in the context of mathematical equations, involves simplifying the expression within the brackets before performing other operations. This follows the order of operations, often remembered by the acronyms BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) or PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

Understanding the Order of Operations

The core principle is to tackle what's inside the brackets first. Then, you proceed according to the remaining order of operations: exponents (if any), multiplication and division (from left to right), and finally addition and subtraction (from left to right).

Example:

Let's solve 2 + 5(8 - 5):

  1. Brackets first: (8 - 5) = 3. The expression now becomes 2 + 5 * 3.
  2. Multiplication: 5 * 3 = 15. The expression simplifies to 2 + 15.
  3. Addition: 2 + 15 = 17. Therefore, the solution is 17.

Different Types of Brackets

While parentheses () are the most common, you may also encounter square brackets [] and curly braces {}. These function identically regarding the order of operations; solve the innermost brackets first and work your way outwards.

Solving Equations with Brackets

Many equations involve brackets. The strategy remains the same: simplify within the brackets first, then apply the remaining order of operations. Sometimes, you might need to distribute a number (expand the brackets) to simplify the expression before proceeding.

Example with Expansion:

Solve 3(x + 2) = 9:

  1. Expand the brackets: 3x + 6 = 9
  2. Subtract 6 from both sides: 3x = 3
  3. Divide both sides by 3: x = 1

Resources for Further Learning

Several online resources can aid your understanding:

  • YouTube Tutorials: Search for "solving equations with brackets" on YouTube for video explanations and examples (example link, another example).
  • Online Math Resources: Websites like Khan Academy offer detailed lessons on order of operations and solving equations.

Remember that consistent application of BODMAS/PEMDAS is key to correctly solving equations with brackets.

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