University:
Santa Ana College
Course:
MATH 083 | Beginning and Intermediate Algebra for Liberal Arts and Social Science
Academic year:

2019
Views:

232

Pages:

3
Author:

Marvin Rowe

Mini-Lecture 1.1 Linear Equations 1. Determine whether a number is a solution to an equation. 2. Solve linear equations. 3. Determine whether an equation is a conditional equation, identity, or contradiction. Preparing for Linear Equations: i) Find the LCD of 5 3 and . 6 4 ii) Simplify: −3(2 x − 5) − 12 − 8 x Examples: 1. Determine which of the numbers are solutions to: 4t − 8 = 7(t + 1) . a) t = 5 b) t = 3 c) t = −15 d) t = −5 STEPS FOR SOLVING A LINEAR EQUATION Step 1: Remove any parentheses using the Distributive Property. Step 2: Combine like terms on each side of the equation. Step 3: Use the Addition Property of Equality to get all variables on one side of the equation and all constants on the other side. Step 4: Use the Multiplication Property of Equality to get the coefficient of the variable to equal . Step 5: Check your answer to be sure that it satisfies the original equation. 2. 2. Solve each linear equation. Be sure to verify your solution. a) 6 x − 5 = − 23 b) −3a + 10 = 8a − 12 c) 7 − 3w + 9 w = 10 + 9 w − 12 d) 4( x + 3) − 2(3 x − 1) = 6 + 4( x − 2) e) 2x + 3 x − 1 5x + = 4 3 2 f) 3p + 1 p −2= 8 6 M-5 g) 2 x x + 1 3x − 2 − = 3 9 6 h) 0.2(3 − x) = −0.4(2x − 4) DEFINITIONS A conditional equation is an equation that is true for some values of the variable and false for other values of the variable. An equation that is satisfied for every choice of the variable for which both sides of the equation are defined is called an identity. An equation that is false for every value of the variable is called a contradiction. 3. Solve and then state whether the equation is conditional, an identity, or a contradiction. a) 3(3 − 4 x) = 4 x − 2(8 x − 3) b) −2 x + 5 − 2 x − 8 = 3 − 4( x + 1) − 2 M-5

Math 083 Linear Eguations

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