University:
Montgomery College
Course:
MATH 130: Elements of Mathematics I: Mathematical Reasoning and Number Systems
Academic year:

2023
Views:

70

Pages:

1
Author:

helyettitycx1

Mini-Lecture 1.4 Introduction to Variable Expressions and Equations Learning Objectives 1. 2. 3. 4. Define and use exponents and the order of operations. Evaluate algebraic expressions, given replacement values for variables. Determine whether a number is a solution of a given equation. Translate phrases into expressions and sentences into equations. Examples: 1. Evaluate. a) 23 b) 17 ⎛6⎞ c) ⎜ ⎟ ⎝7⎠ 2 d) (0.3)3 Using order of operation, simplify each expression. e) 7 + 3 · 2 f) 25 – 32 · 2 g) 6[-5 + 6(-3 + 8)] h) 20(−1) − (−4)(−3) 2[−12 ÷ (−3 − 3)] d) 5z 3 y2 − x z d) y = 3y + 2; 0 2. Evaluate each expression when x = 3, y = 2, and z = 6. a) x + y + z b) 3x – z c) 5x − 2 z 3. Determine whether the given number is a solution of the given equation. 3 15 x= a) x – 12 = 15 ; 27 b) 12 + y = 29; 7 c) ; 5 4 20 4. Write each phrase as an algebraic expression. a) The sum of a number and thirteen b) The quotient of forty-two and a number Write each sentence as an equation. c) The product of one-third and a number is nine d) A number added to twelve is fourteen. Teaching Notes: • • • • • Be sure to identify base and exponent when working with exponential notation. Most students find order of operations challenging. Many students will confuse expression and equation. Be sure students understand that you simplify an expression, but solve an equation. Many students have problems with translating sentences into equations. Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) 8; 1b) 1; 1c) 36/49; 1d) 0.027; 1e) 13; 1f) 7;1g) 150; 1h) -8; 2a) 11; 2b) 3; 2c) 3; 2d) 8; 3a) true; 3b) false; 3c) false; 3d) false; 4a) x + 13; 4b) 42/x; 4c) 1/3 x = 9; 4d) 12 + x = 14