Substitution turns letters into numbers
To evaluate an expression is to find its number once you know the value of each variable. The tool is substitution: you replace every copy of the variable with its value — wrapped in parentheses — and then it is pure arithmetic. The parentheses are not optional; they protect signs and powers.
Then follow the order of operations
Once the numbers are in, simplify with the order of operations (PEMDAS): parentheses, exponents, then multiplication and division left to right, then addition and subtraction left to right. Work one operation at a time and write each line out — speed comes from clarity, not from skipping steps.
Evaluate 2x^2 - 5x + 1 at x = -3 = 2(-3)^2 - 5(-3) + 1 substitute, with parentheses = 2(9) - 5(-3) + 1 exponent first: (-3)^2 = 9 = 18 + 15 + 1 multiply: 2*9=18, -5*(-3)=+15 = 34 add left to right
Evaluation as a check
- Suppose you simplified 2(3x - 1) + 4(x + 2) to 10x + 6 in the last guide and want to be sure.
- Pick any value, say x = 5. Evaluate the original: 2(15 - 1) + 4(5 + 2) = 2(14) + 4(7) = 28 + 28 = 56.
- Evaluate the simplified form: 10(5) + 6 = 56. They match, so the two are very likely equivalent expressions.