Exercise 8 Page 30

Write two separate equations.

x=7 and x=- 3

Practice makes perfect

When the absolute values of two expressions are equal, either the expressions are equal or the opposites of the expressions are equal. Let's look at an example equation. |ax+b|=|cx+d| For this equation, there are two possible cases to consider. ax+b=cx+d or ax+b=- (cx+d) To solve the given absolute value equation, we will write two equations similar to those above when we remove the absolute value.

|x+8|=|2x+1|

lc x+8 ≥ 0:x+8 = (2x+1) & (I) x+8 < 0:x+8 = - (2x+1) & (II)

lcx+8=2x+1 & (I) x+8=- (2x+1) & (II)

Distr

(II):Distribute -1

lx+8=2x+1 x+8=- 2x -1

(I), (II):LHS-8=RHS-8

lx=2x-7 x=- 2x -9

SubEqn

(I):LHS-2x=RHS-2x

l- x=- 7 x=- 2x -9

DivEqn

(I):.LHS /- 1.=.RHS /- 1.

lx=7 x=- 2x -9

AddEqn

(II):LHS+2x=RHS+2x

lx=7 3x=- 9

DivEqn

(II):.LHS /3.=.RHS /3.

lx_1=7 x_2=- 3

After solving an absolute value equation, it is necessary to check for extraneous solutions. To do this, we substitute the found solutions into the given equation and determine if a true statement is made.

|x+8|=|2x+1|

Substitute

x= 7

| 7+8|? =|2( 7)+1|

Multiply

|7+8|? =|14+1|

AddTerms

Add terms

|15|? =|15|

AbsPos

|15|=15

15=15 ✓