Replace variables and keep the operations

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Replace variables and keep the operations

Substitution assigns a stated number to each variable without changing the structure of the expression. Use brackets when replacing a letter with a negative value. This prevents a minus sign from being mistaken for an operation outside a power.

Scientific formulae also need consistent units. In s = ut + (1/2)at², a time in seconds must fit the units of velocity and acceleration. Calculate powers before multiplication, retain working precision, and interpret the answer in the quantity requested.

A formula can give different answers as its inputs vary; substitution evaluates one particular case. Check the result against an estimate or the original context, especially where a measurement cannot sensibly be negative.

Worked example: Evaluate 2x²−3x when x=−2.

Substitute with brackets: 2(−2)²−3(−2).

The square is 4, so the first term is 8.

The second term is −(−6), which adds 6.

Answer: 14.

Check your understanding: What is 3x+2 when x=4?

Answer: 14.

Why: Multiply 3 by 4 before adding 2.