Question

what is the solution to the linear equation?
$4b + 6 = 2 - b + 4$
options: $b = 4$, $b = 6$, $b = 0$, $b = -2$

Explanation:

Step1: Simplify the right side

First, combine the constant terms on the right side of the equation \(4b + 6 = 2 - b + 4\). The constants \(2\) and \(4\) can be added together. So, \(2 + 4 = 6\), and the equation becomes \(4b + 6 = 6 - b\).

Step2: Add \(b\) to both sides

To get all the \(b\) terms on one side, we add \(b\) to both sides of the equation. This gives us \(4b + b + 6 = 6 - b + b\). Simplifying both sides, we have \(5b + 6 = 6\).

Step3: Subtract 6 from both sides

Next, we subtract \(6\) from both sides to isolate the term with \(b\). So, \(5b + 6 - 6 = 6 - 6\), which simplifies to \(5b = 0\).

Step4: Divide by 5

Finally, we divide both sides of the equation by \(5\) to solve for \(b\). That is, \(\frac{5b}{5}=\frac{0}{5}\), so \(b = 0\).

Answer:

\(b = 0\) (corresponding to the option "b = 0")