EZ Math

Pre-Algebra · Order of operations

How to Evaluate an Algebraic Expression

Problem

2x2+3x−1, where x=32x^2 + 3x - 1, \text{ where } x = 3

Answer

2626

An algebraic expression has numbers, variables and operations. To evaluate it, replace each variable with the given number, then work through the order of operations.

Step-by-step solution

  1. Replace every x with 3.

    2(3)2+3(3)−12(3)^2 + 3(3) - 1

    Why: The value of the expression depends on the value of x.

  2. Apply the exponent.

    2(9)+3(3)−12(9) + 3(3) - 1

    Why: Exponents come before multiplication.

  3. Multiply.

    18+9−118 + 9 - 1

    Why: Multiplication comes before addition and subtraction.

  4. Add and subtract from left to right.

    27−1=2627 - 1 = 26

    Why: The expression now has one value.

Common mistakes

  • Squaring 2 and x together: 2x means 2 times x, not (2x) squared.
  • Reading 3x as 3 + x. The number and the letter mean multiplication.
  • Doing 18 + 9 - 1 as 18 + 8. Subtraction also goes left to right.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

  1. 2x+1, where x=52x + 1, \text{ where } x = 5

    Show answer

    1111

  2. x2, where x=6x^2, \text{ where } x = 6

    Show answer

    3636

  3. 3x−4, where x=23x - 4, \text{ where } x = 2

    Show answer

    22

  4. x2+2x, where x=4x^2 + 2x, \text{ where } x = 4

    Show answer

    2424

  5. 5x−2x, where x=35x - 2x, \text{ where } x = 3

    Show answer

    99