3b/7 – 1 =5. What is “b”?
The Correct Answer and Explanation is:
To solve the equation ( \frac{3b}{7} – 1 = 5 ), we can follow these steps to isolate ( b ):
Step 1: Isolate the Fraction
Start by adding ( 1 ) to both sides of the equation to eliminate the constant on the left side:
[
\frac{3b}{7} – 1 + 1 = 5 + 1
]
This simplifies to:
[
\frac{3b}{7} = 6
]
Step 2: Eliminate the Fraction
Next, we want to eliminate the fraction by multiplying both sides of the equation by ( 7 ):
[
7 \cdot \frac{3b}{7} = 6 \cdot 7
]
This simplifies to:
[
3b = 42
]
Step 3: Solve for ( b )
Now, we divide both sides by ( 3 ) to solve for ( b ):
[
b = \frac{42}{3}
]
Calculating this gives:
[
b = 14
]
Conclusion
Thus, the solution to the equation ( \frac{3b}{7} – 1 = 5 ) is ( b = 14 ).
Explanation of the Process
When solving linear equations, the goal is to isolate the variable, in this case, ( b ). We performed operations that kept the equation balanced, following the principle that whatever we do to one side of the equation must also be done to the other side. By first eliminating the constant, we simplified our work with the variable. Multiplying both sides by ( 7 ) removed the fraction, making it easier to isolate ( b ). Finally, dividing by ( 3 ) yielded the value of ( b ). This method can be applied to various algebraic equations, reinforcing foundational skills in algebra and promoting confidence in problem-solving techniques. Understanding each step aids in solving more complex equations and developing mathematical reasoning.