Select the correct answer.
What is the justification for step 4 in the solution process?
Step 1 : [tex]\frac{9}{2} b+11-\frac{5}{6} b=b+2[/tex]
Step 2 : [tex]\frac{22}{6} b+11=b+2[/tex]
Step 3 : [tex]\frac{8}{3} b+11=2[/tex]
Step 4 : [tex]\frac{8}{3} b=-9[/tex]
[tex]b=-\frac{27}{8}[/tex]
A. combining like terms
B. the multiplication property of equality
C. the subtraction property of equality
D. the addition property of equality
Answer (2)
To isolate the term with 'b' in the equation, subtract 11 from both sides.
Apply the subtraction property of equality to maintain the balance of the equation.
Simplify the equation to get 3 8 b = − 9 .
The justification for step 4 is the subtraction property of equality, so the answer is C.
Explanation
Understanding the Problem The problem asks us to identify the justification for step 4 in the given solution process. We need to analyze how step 4 is derived from step 3.
Isolating the Term with 'b' Step 3 states: 3 8 b + 11 = 2 Step 4 states: 3 8 b = − 9 To get from step 3 to step 4, we need to isolate the term with 'b' on one side of the equation. This can be done by subtracting 11 from both sides of the equation.
Performing the Subtraction Subtracting 11 from both sides of the equation in Step 3: 3 8 b + 11 − 11 = 2 − 11 3 8 b = − 9
Identifying the Justification The operation performed is subtracting 11 from both sides of the equation. This is justified by the subtraction property of equality, which states that if you subtract the same value from both sides of an equation, the equation remains balanced. Therefore, the correct answer is C.
Examples
The subtraction property of equality is a fundamental concept in algebra. It's used in various real-life scenarios, such as balancing budgets. For example, if you have a certain amount of money and you spend some, you subtract that amount from your initial balance to find out how much you have left. Similarly, in physics, when calculating net force, you subtract opposing forces to find the resultant force. Understanding this property helps in solving equations and understanding relationships between quantities.
The justification for step 4 in the solution process is the subtraction property of equality, which allows us to subtract the same value from both sides of the equation while keeping it balanced. By subtracting 11 from both sides of step 3, we isolate 'b' and reach the equation in step 4. Therefore, the correct answer is C.
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