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3.1 Variables and Algebraic Expressions (AM) Essential Question: How can you use algebraic expressions to solve problems? To evaluate an algebraic expression, substitute the value(s) of the variable(s) into the expression, identify each term in the expression and describe what it represents. You can express unknown quantities with variables in algebraic expressions, and when given values for the variables, you can evaluate the expressions. A numerical expression ( ex. 7 – 5) contains only numbers and operations, while an algebraic expression( exs. 3b – 2, 5x𝑣 5 ) also contains at least one variable. An expression is a mathematical phrase that contains operations, numbers, and/or variables. The number in directly in front of the variable is called the coefficient. In the expression 7m, 7 is the coefficient. Terms are the parts of an expression that are added or subtracted. In the expression 8n3p, 8n is one term and 3p is another term. *A real-world expression also contains units of measurement. Expressions are evaluated not solved!!! Equivalent expressions are created when you evaluate them or simplify them. Ex. 4x + 7x = 11x ex. Both sides represent equivalent expressions Example 1: Evaluate each algebraic expression below if 𝑛 = 17, 𝑟 = 9, 𝑦 = 2.4, 𝑧 = 7.89, 𝑎𝑛𝑑 𝑠 = 0.92 a. 𝑛 + 8 b. 𝑧 − 𝑠 c. 2 𝑟 3 d. 𝑦 3 Example 2: 3 3 Evaluate the algebraic expression 𝑥𝑦𝑧 if 𝑥 = 4 , 𝑦 = 28, 𝑎𝑛𝑑 𝑧 = 7 Example 3: Evaluate 𝑘−𝑚 ℎ 3 1 1 if 𝑘 = 7 4 , 𝑚 = 4 , 𝑎𝑛𝑑 ℎ = 8 2 1 Example 4: Evaluate each expression if 𝑎 = −3 𝑏 = 2 𝑐 = 3 𝑑 = − 2 𝑎𝑐(𝑏 + 𝑑) 2 Example 5: Evaluate each expression if 𝑤 = 5 𝑥 = −6 𝑦 = 3 𝑧 = −2 w𝑥𝑦 ÷ 𝑧