What is the solution to the linear equation?
$4 b+6=2-b+4$
A. $b=-2$
B. $b=0$
C. $b=4$
D. $b=6$
Answer (1)
Combine like terms: Rewrite the equation as 4 b + 6 = 6 − b .
Isolate the variable: Add b to both sides to get 5 b + 6 = 6 .
Solve for b : Subtract 6 from both sides to get 5 b = 0 , then divide by 5 to find b = 0 .
The solution is: 0 .
Explanation
Understanding the Problem We are given the linear equation 4 b + 6 = 2 − b + 4 and asked to find the value of b that satisfies the equation. We will solve this equation step-by-step.
Simplifying the Equation First, we simplify the right side of the equation by combining like terms: 2 − b + 4 = 6 − b . So the equation becomes 4 b + 6 = 6 − b .
Isolating the Variable Next, we want to isolate the variable b on one side of the equation. To do this, we add b to both sides of the equation: 4 b + 6 + b = 6 − b + b , which simplifies to 5 b + 6 = 6 .
Further Isolation Now, we subtract 6 from both sides of the equation: 5 b + 6 − 6 = 6 − 6 , which simplifies to 5 b = 0 .
Solving for b Finally, we divide both sides of the equation by 5 to solve for b : 5 5 b = 5 0 , which simplifies to b = 0 .
Final Answer Therefore, the solution to the linear equation is b = 0 .
Examples
Linear equations are used in various real-life scenarios, such as calculating the cost of items, determining distances, and converting units. For example, if you want to determine how many hours you need to work to earn a certain amount of money, you can set up a linear equation to model the situation and solve for the number of hours. Understanding how to solve linear equations is a fundamental skill in mathematics and has practical applications in everyday life.
