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Chapter 2: Q5 (page 41)

Justify each step.

23b=8鈭�2b

2b=38鈭�2b

2b=24鈭�6b

8b=24

b=3

Short Answer

Expert verified

23b=8鈭�2bGiven

2b=38鈭�2bMultiplication property of equality

2b=24鈭�6bDistributive property

8b=24Addition property of equality.

b=3 Division property of equality

Step by step solution

01

Step 1. Apply the multiplication property of equality.

If p=qthen, rp=rq.

02

Step 2. Description of step.

Multiply each side of the 23b=8鈭�2bby 3 and simplify.

3脳23b=38鈭�2b2b=38鈭�2b

03

Step 3. Apply distributive property.

Expand the right-hand side of the equation obtained in step 2 using the distributive property.

2b=3脳8鈭�3脳2b=24鈭�6b

04

Step 4. Apply the addition property of equality.

If p=qand r=s, then p+r=q+s.

05

Step 5. Description of step.

Add 6bon each side of 2b=24鈭�6band simplify.

2b+6b=24鈭�6b+6b

8b=24

06

Step 6. Apply division property of equality.

If p=qand r鈮�0, then pr=qr.

07

Step 7. Description of step.

Divide each side of the equation obtained in steps 5 by 8 to find the value of b.

8b8=248b=3

Therefore, the value of b is 3.

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