Mathematics (Core)Exam code: 0580
Linear Equations
Algebra and Sequences
Building the statement
- An equation needs two expressions for the same quantity, set equal
- Read the sentence for the fact that links them: a total, a perimeter, an angle sum, or two costs being equal
- Check the expression before solving by substituting a trial value
Exam tip
Solve the equation you wrote
In a question that asks you to form an equation and solve it, the method marks for solving it follow through from your own equation. A correct first step, and a correct line such as 4x = 28 that it simplifies to, each still score even if the equation itself was wrong. So never stop after forming it: write the equation on its own line, as it earns marks too, then solve it step by step.
Worked example
Consecutive integers
Three consecutive integers have a sum of 84. Find the integers.
Solution:
- Name the unknown first, and choose the one the others can be written from
- Let the smallest integer be n
- Consecutive means each is one more than the last, so the other two are n + 1 and n + 2
- Writing all three in terms of a single letter is what makes this solvable with one equation
- Their sum is 84, which gives n + (n + 1) + (n + 2) = 84
- Collect the three n terms and the two numbers: 3n + 3 = 84
- Subtract 3 from both sides: 3n = 81
- Divide by 3: n = 27
- The integers are 27, 28 and 29
- Answer the question rather than stopping at n = 27, and check: 27 + 28 + 29 = 84