Solving Equations with Absolute Values August 25th, 2016

Absolute Value The absolute value of a number is its distance from 0 on the number line. Since distance is nonnegative, the absolute value of a number is always nonnegative. The symbol 𝑥 is used to represent the absolute value of a number x. Example: −3 =3 and 3 =3 3 units 3 units -4 -3 -2 -1 0 1 2 3 4

Evaluating an Expression with an Absolute Value Example: Evaluate 1.4 + 5𝑦 −7 if 𝑦=−3 1.4+ 5𝑦−7 =1.4+ 5 −3 −7 Replace y with -3 =1.4+ −15 −7 Simplify 5(-3) first. =1.4+ −22 Subtract 7 from -15 =1.4+22 −22 =22 =23.4 Add.

Absolute Value Equations Some equations contain absolute value expressions. The definition of absolute value is used in solving these equations. Note 𝑥 =5 𝑥=5 𝑜𝑟 −5

Solve an Absolute Value Equation Solve 𝑥−18 =5. Check your solutions Note: There are two parts to every absolute value equation, so we will look at each part individually.

Solve 𝑥−18 =5 Case 1 𝑥−18=5 𝑥−18+18=5+18 𝑥=23 Check: 𝑥−18 =5 23−18 =5 5 =5 5=5

Solve 𝑥−18 =5 Case 2 𝑥−18=−5 𝑥−18+18=−5+18 𝑥=13 Check: 𝑥−18 =5 13−18 =5 −5 =5 5=5

You try! (REMEMBER TO CHECK YOUR ANSWERS!) 𝑥−25 =17 2 𝑏+4 =48 𝑥={8, 42} 𝑏={−28, 20}