Algebra as Language Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Express in algebra: 'The product of two consecutive integers is 12 more than twice their sum.'

Solution

  1. 1
    Step 1: Let the integers be nn and n+1n+1.
  2. 2
    Step 2: Product: n(n+1)n(n+1). Sum: n+(n+1)=2n+1n + (n+1) = 2n+1.
  3. 3
    Step 3: Equation: n(n+1)=2(2n+1)+12n(n+1) = 2(2n+1) + 12.
  4. 4
    Step 4: Simplify: n2+n=4n+2+12n^2 + n = 4n + 2 + 12, so n2−3n−14=0n^2 - 3n - 14 = 0.

Answer

n2−3n−14=0n^2 - 3n - 14 = 0
Complex word problems become manageable once translated into algebra. Naming variables, expressing relationships, and setting up equations is the language of algebra at work.

About Algebra as Language

The perspective that algebra is a formal language with syntax and grammar for expressing mathematical ideas and relationships precisely.

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More Algebra as Language Examples

Example 1 easy

Translate into algebra: 'Five more than twice a number is seventeen.'

Example 3 easy

Write an equation: 'A number decreased by 7 equals 15.'

Example 4 medium

Express: 'The square of the sum of [formula] and [formula]' vs 'The sum of the squares of [formula]

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