REMINDER When you go to the open lab next door in 203 please make sure you sign in on the log sheet and enter your instructor s name and your section number We need to collect this information to document lab usage and ensure future funding for tutors Removable stickers with tutoring schedules are still available If you haven t gotten one yet get one from the TA now and stick it on your laptop Emergency Log In The next few slides has the information for an emergency log in site to access homework practice quizzes etc Since the Course Compass features are being converted to Pearson MyLab and Mastering a new emergency log in site may be available later in the semester For now we will use the following Any questions on the Section 1 4 homework that was due today Now please CLOSE YOUR LAPTOPS and turn off and put away your cell phones Sample Problems Page Link Dr Bruce Johnston Section 2 1 Linear Equations in One Variable Section 2 1 An algebraic equation is a statement that two expressions have equal value Solving algebraic equations involves finding values for a variable that make the equation true Equivalent equations are equations with the same solutions Example x 1 5 and 3x 1 19 are equivalent equations because plugging in x 6 makes both of them true A linear equation in one variable can be written in the form ax b c a 0 Examples 3x 2 8 5x 7 14 29 8y 71 12z 100 Solving linear equations in one variable 1 2 3 4 5 Multiply to clear fractions if there are any Simplify each side of equation by distributing where necessary and then combining like terms Get all variable terms on one side and number terms on the other side of equation addition property of equality Get variable alone multiplication property of equality ALWAYS check solution by substituting into original problem Sample problems link Example 1 Solve 8 z 8 8 8 z 8 8 z 16 Add 8 to each side Simplify both sides NOW CHECK plug z 16 into the ORIGINAL equation 8 z 8 8 16 8 Example 2 Solve 3a 2a 7 4a 5a 7 4a Simplify the left side 5a 4a 7 4a 4a a 7 Simplify both sides NOW CHECK Add 4a to each side 4p 11 p 2 2p 20 3p 11 2p 18 Simplify both sides 3p 2p 11 2p 2p 18 p 11 18 Add 2p to both sides Simplify both sides p 11 11 18 11 Add 11 to both sides p 7 Simplify both sides NOW CHECK Plug in 7 everywhere there s a p in the original equation and see if both sides simplify to the same number 5 3 z 8z 9 4z 15 5z 8z 9 4z Use distributive property 6 3z 4z Simplify left side 6 3z 4z 4z 4z 6 z 0 Simplify both sides 6 6 z 0 6 z 6 Add 4z to both sides Add 6 to both sides Simplify both sides NOW CHECK y 8 1 y 8 1 y 8 NOW CHECK multiply both sides by 1 simplify both sides 1 5 x 7 9 1 5 7 x 7 7 9 multiply both sides by 7 35 simplify both sides x 9 NOW CHECK Sample problem from today s homework Answer 46 9 Make sure you check your answer This one can be checked fairly quickly using a calculator Make sure you put parentheses around expressions in numerators before you divide by the denominator because calculators follow the order of operations exactly Sample problem from today s homework 5x 5 2 x 1 3x 7 5x 5 2x 2 3x 7 use distributive property 5x 5 5x 5 simplify the right side Both sides of the equation are identical Since this equation will be true for every x that is substituted into the equation the solution is all real numbers This equation is an example of an identity Note that if you continued to solve this equation by subtracting 5x from both sides and adding 5 to both sides you would come up with 0 0 Whenever you get this result the answer is all real numbers which is NOT the same thing as x 0 3x 7 3 x 1 3x 7 3x 3 use distributive property 3x 3x 7 3x 3x 3 add 3x to both sides 7 3 simplify both sides Since no value for the variable x can be substituted into this equation that will make this a true statement there is no solution This equation is an example of a contradiction Sample problem from today s homework Answer R Reminder This homework assignment on section 2 1 is due at the start of next class period You may now OPEN your LAPTOPS and log in to CourseCompass