Exercise 44 Page 67

An absolute value measures an expression's distance from a midpoint on a number line. |3x+9|= 11 This equation means that the distance is 11, either in the positive direction or the negative direction.

|3x+9|= 11 ⇒ l3x+9= 11 3x+9= - 11 To find the solutions to the absolute value equation, we need to solve both of these cases for x. Let's approach them one at a time.

Case 1

To solve the equation we will isolate x on one side using the Properties of Equality.

3x+9=11

SubEqn

LHS-9=RHS-9

3x=2

DivEqn

.LHS /3.=.RHS /3.

x=2/3

The first solution is 23.

Case 2

Again, we will isolate x on one side of the equation.

3x+9=- 11

SubEqn

LHS-9=RHS-9

3x=- 20

DivEqn

.LHS /3.=.RHS /3.

x=- 20/3

MoveNegNumToFrac

Put minus sign in front of fraction

x=-20/3

The second solution is - 203.