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Evaluating Expressions

In this lesson you’ll learn how to evaluate algebraic expressions by replacing variables with given numbers and following the order of operations.

Evaluating an expression means plugging in a specific value for each variable and computing the result, just like following a recipe with exact amounts.

Steps:

  1. Replace every instance of the variable with the given number (use parentheses if needed to avoid confusion).
  2. Follow order of operations: Parentheses → Exponents → Multiply/Divide (left to right) → Add/Subtract (left to right).

Example: Evaluate 2x+3y2x + 3y when x=5x = 5 and y=4y = 4

2(5)+3(4)=10+12=222(5) + 3(4) = 10 + 12 = 22

Another: 5+4n5 + 4n when n=3n = 3

5+4(3)=5+12=175 + 4(3) = 5 + 12 = 17

Evaluate 72a+b7 - 2a + b when a=6a = 6 and b=9b = 9

  1. Substitute: 72(6)+97 - 2(6) + 9
  2. Multiply first: 712+97 - 12 + 9
  3. Add/subtract left to right: 5+9=4-5 + 9 = 4

Final result: 44

Evaluating expressions helps calculate costs or totals when you know the values. Example: Monthly phone bill = 30 dollars base + 0.05 dollars per text. If you send 400 texts: 30+0.05(400)=30+20=5030 + 0.05(400) = 30 + 20 = 50 dollars. Or fuel cost = 3.50 dollars per gallon × g gallons. Plug in g = 12 for 42 dollars.

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