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

2023
Views:

317

Pages:

1
Author:

Dominick Dickson

Mini-Lecture 2.4 Solving Linear Equations Learning Objectives: 1. 2. 3. 4. Apply a general strategy for solving a linear equation. Solve equations containing fractions. Solve equations containing decimals. Recognize identities and equations with no solution. Examples: 1. Solve the following linear equations. a) 6a – (5a – 1) = 4 b) 4(3b – 1) = 16 c) 4z = 8(2z + 9) d) e) 3(2a – 3) = 5(a + 4) f) 12(4c – 2) = 3c – 4 2(x + 8) = 3(x – 5) 2. Solve each equation containing fractions. a) y − 4 =1 6 b) 1 3 x− x=5 4 8 c) −6 x + 5 5x +1 = − 4 4 Solve each equation containing decimals. d) 0.05 x + 0.06( x − 1,500) = 570 e) 0.4(x + 7) –0.1(3x + 6) = -0.8 3. Solve each equation. Indicate if it is an identity or an equation with no solution. a) 6(z + 7) = 6z + 42 b) 3 + 12x – 1 = 8x +4x – 1 c) x 2x −3= +1 3 6 Teaching Notes: • • • • • Refer students to the beginning of this section in the textbook for steps: To Solve Linear Equations in One Variable. Most students find solving equations with fractions or decimals difficult. Common error: When multiplying equations with fractions by the LCD, some students multiply only the terms with fractions instead of all terms. Common error: When solving equations with decimals and parentheses (examples 2d and 2e), some students multiply terms both inside parentheses and outside parentheses by a power of 10. Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) 3; 1b) 5/3; 1c) -6; 1d) 31; 1e) 29; 1f) 4/9; 2a) 30; 2b) -40; 2c) 9; 2d) 6,000 2e) -30; 3a) identify; 3b) no solution; 3c) no solution