Evaluating expressions with a variable

Evaluating expressions with a variable

Evaluating expressions with a variable

To evaluate an expression means to compute its value once you know the variable. Substitute the number for the letter and follow the order of operations.

The method

  1. Replace each occurrence of the variable with the given number.
  2. Use the order of operations: brackets first, then multiplication/division, then addition/subtraction.

Examples

Evaluate `3x + 4` when `x = 5`.
  1. Substitute: `3 · 5 + 4`.
  2. Multiply first: `15 + 4`.
  3. Add: 19.
Evaluate `2a − 7` when `a = 6`.
  1. Substitute: `2 · 6 − 7`.
  2. Multiply: `12 − 7`.
  3. Subtract: 5.
Evaluate `n ÷ 3 + 8` when `n = 12`.
  1. Substitute: `12 ÷ 3 + 8`.
  2. Divide: `4 + 8`.
  3. Add: 12.

Order of operations — reminder

Brackets → exponents → multiplication/division → addition/subtraction.

Operations at the same level go left-to-right.

Common traps

  • 3x means 3 · x. Many beginners write `35` for `3x` when `x = 5`. The correct value is `3 · 5 = 15`.
  • Sign of the variable. If `x = −4`, the expression `2x + 1` is `2 · (−4) + 1 = −7`. Use brackets when substituting a negative.
  • Order matters. `3 + 4 · 2` is `3 + 8 = 11`, not `(3 + 4) · 2 = 14`.

Try it out