Exercise 15 Page 32

An absolute value measures an expression's distance from a midpoint on a number line. |m+3|= 7 This equation means that the distance is 7, either in the positive direction or the negative direction. |m+3|= 7 ⇒ lm+3= 7 m+3= - 7 To find the solutions to the absolute value equation, we need to solve both of these cases for m.

| m+3|=7

lc m+3 ≥ 0:m+3 = 7 & (I) m+3 < 0:m+3 = - 7 & (II)

lcm+3=7 & (I) m+3=- 7 & (II)

(I), (II): LHS-3=RHS-3

lm_1=4 m_2=- 10

Both 4 and - 10 are solutions to the absolute value equation. Let's graph these solutions on a number line.