Solving linear equations - OCRSolving equations with unknowns on both sides
Forming, using and solving equations are skills needed in many different situations. From balancing accounts to making sense of a mobile phone bill, solving equations is a vital skill.
Some equations have letters on each side of the equals sign, for example: \(4(k + 7) = 12k - 4\)
Solve this equation by rearranging all the letters onto one side of the equation and all numbers onto the other side. The easiest way to do this is usually by moving the unknown with the smallest coefficient in the equation (the letter with the smallest number in front of it).
Example
Solve \(4(k + 7) = 12k - 4\).
Expand the bracket:
\(4k + 28 = 12k - 4\)
Decide which of the unknowns has the smallest number in front of it. 4 is less than 12 so subtract \(4k\) from each side.
\(4k + 28 - 4k = 12k - 4 - 4k\)
\(28 = 8k - 4\)
Isolate the term \(28 + 4 = 8k - 4 + 4\)
\(32 = 8k\)
Isolate \(k\) by dividing each side by 8:
\(32 \div 8 = 8k \div 8\)
\(4 = k\)
Substituting \(k = 4\) back into the original equation gives: