1 College Algebra K/DC Friday, 23 October 2015 OBJECTIVE TSW review terminology of equations, solve linear equations, and identify equations as identities, conditionals, or contradictions. TESTS are graded. TODAY’S ASSIGNMENT (due on Monday, 10/26/15) –Sec. 1.1: pp (9-35 odd)

1-2 Write the problem and solve each equation. Use solution sets. 9)11) 13)15) 17)19) 21)23) 25)27) Write the problem. Decide whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set. 29)31) 33)35) If you finish today, keep it until Monday. Due Monday, 10/26/15 Assignment: Sec. 1.1: pp (9–35 odd) Due Monday, 10/26/15

Solving Linear Equations 1.1

Terminology An equation is a statement that two expressions are equal. To solve an equation means to find all numbers that make the equation true. These numbers are the solutions or roots of the equation. A number that is a solution satisfies the equation. The solution(s) of an equation make up its solution set. Equations with the same solution set are equivalent equations.

1-5 Solve. Solving a Linear Equation Solution set: {6} Distributive property Combine terms. Add 4 to both sides. Add 12x to both sides. Combine terms. Divide both sides by 4. NOTE: You are solving an equation; Use solution sets!

1-6 Solve. Clearing Fractions Before Solving a Linear Equation Solution set: {–10} Multiply by 10, the LCD of all the fractions. Distributive property Combine terms. Add –4s and –6 to both sides. Combine terms. Divide both sides by –6.

1-7 Solve Clearing Decimals Before Solving a Linear Equation Solution set: {12} Multiply both sides by 10 (one decimal place). Distribute on the right side. Add 12 and subtract 4x from both sides. Divide both sides by 4.

Types of Equations An identity is an equation that leads to a true statement. –It can be simplified to 0 = 0. –The solution set is {all real numbers}, or ℜ. A conditional equation is an equation whose solution is a single number. –Ex: x = 3 –Braces are used to indicate solutions { }. A contradiction is an equation that leads to a false statement. –Ex: –3 = 7 –The solution set is the empty set, or Ø but it is NOT {Ø}.

1-9 Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. Identifying Types of Equations This is a conditional equation. Solution set: {11} Add –4x and 9 to both sides. Combine terms. Divide both sides by 2.

1-10 Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. Identifying Types of Equations This is a contradiction. Solution set: ø Distributive property Subtract 14x from both sides.

1-11 Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. Identifying Types of Equations This is an identity. Solution set: {all real numbers} Distributive property Combine terms. Add x and –3 to both sides. The most common mistake on this type of problem is to forget to state the solution set !

1-12 Write the problem and solve each equation. Use solution sets. 9)11) 13)15) 17)19) 21)23) 25)27) Write the problem. Decide whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set. 29)31) 33)35) If you finish today, keep it until Monday. Due Monday, 10/26/15 Assignment: Sec. 1.1: pp (9–35 odd) Due Monday, 10/26/15

13 College Algebra K/DC Monday, 26 October 2015 OBJECTIVE TSW solve equations for a specified variable. ASSIGNMENT DUE (wire basket) –Sec. 1.1: pp (9-35 odd) TODAY’S ASSIGNMENT (due Wed/Thur) –Sec. 1.1: p. 85 (39-47 all, all)

Due Wednesday/Thursday, 28/29 October Assignment: Sec. 1.1: p. 85 (39-47 all, all) Due Wednesday/Thursday, 28/29 October Write each problem. Then, solve for the indicated variable. Write each problem. Then, solve for x.

15 Solving For a Specified Variable 1.1

2-16 Solve for the specified variable. Solving for a Specified Variable (a) d = rt, for t (b), for k Divide both sides by r. Factor out k. Divide both sides by

2-17 Solve for the specified variable. Solving for a Specified Variable (c), for y Distributive property Subtract 8y and 8 from both sides. Divide both sides by 3.

1-18 Write each problem and solve. Leave answers as fractions when necessary. Use solution sets Class Problems – Sec. 1.1 (10/26/2015) (Due today – show work)  Bring to me, please. Write the equation and solve. Idenitfy as an identity, conditional, or contradiction. Give the solution set. Write the equation and solve for the indicated variable. Use solution sets.

Due Wednesday/Thursday, 28/29 October Assignment: Sec. 1.1: p. 85 (39-47 all, all) Due Wednesday/Thursday, 28/29 October Write each problem. Then, solve for the indicated variable. Write each problem. Then, solve for x.