Exercise 19 Page 231

Before we can solve this equation, we need to isolate the absolute value expression using the Properties of Equality. An absolute value measures an expression's distance from a midpoint on a number line. |2x-7|= 4 This equation means that the distance is 4, either in the positive direction or the negative direction. |2x-7|= 4 ⇒ l2x-7= 4 2x-7= - 4 To find the solutions to the absolute value equation, we need to solve both of these cases for x.

| 2x-7|=4

lc 2x-7 ≥ 0:2x-7 = 4 & (I) 2x-7 < 0:2x-7 = - 4 & (II)

lc2x-7=4 & (I) 2x-7=- 4 & (II)

(I), (II): LHS+7=RHS+7

l2x=11 2x=3

(I), (II): .LHS /2.=.RHS /2.

lx_1= 112 x_2= 32

Both 112 and 32 are solutions to the absolute value equation.