Linear Equations in One Variable Sec. 1.2 Linear Equations in One Variable

Equation Solve Solution Two alg. Expressions that are equal Find values for which x is true Solution The values that make the equation true

Identity Equation An equation that is true for every real number in the domain Ex. X2 – 9 = (x+3)(x-3)

Conditional Equations Equation that is true for some (or none) of the real numbers in the domain Ex. X2-9=0 Only solutions are 3 and -3 so conditional

Linear equation in 1 variable Standard form ax+b=0 a & b are real numbers, a≠0 Has exactly 1 solution (when our y value is 0) X intercept

Solve Ex. 3x-6=0

Some equations have no solution You will get a false statement such as 0=5 x=x+1 has no solution

Ex. 2 6(x-1)+4=3(7x+1) How can you check your answer? Substitute back in

Ex. 3(x+3)=5(1-x)-1 b) (x+1)2+2(x-2)=(x+1)(x-2)

Try 3(x+2)-5=3x+1

Involving fractions Find the LCD and multiply every term in the equation by the LCD Ex. 3

Ex. 4

Extraneous solution One that does not satisfy the original equation (occurs when you multiply or divide an equation by a variable quanity)

Single fractions on each side can be done by cross multiplying

HW P. 93 1-19 odd, 23-37 odd, 43-91odd, 94