91Ó°ÊÓ

When solving an equation, the first step is often to isolate the variable. This means getting the variable, like \( b \), all by itself on one side of the equation. To do this, you'll need to move other terms (usually constants) to the opposite side.
In the given exercise, we started with the equation \[-77 = 9b - 5\]. The constant term \-5\ is on the same side as the variable term \( 9b \). To isolate \( b \), we move that constant term to the other side. We do this by adding \+5\ to both sides: \[-77 + 5 = 9b - 5 + 5\]. This results in the simplified equation \-72 = 9b\, leaving the variable term alone on one side. By moving terms step-by-step, we make it easier to find the solution.

Sometimes equations have constants on both sides, which can make them look complicated. You can handle this by performing basic arithmetic operations to combine or move these constants.
In our example, the original equation was \[-77 = 9b - 5\]. This can seem tricky because of constants on both sides. By adding \+5\ to both sides, we effectively neutralize the \-5\ and simplify the equation to \-72 = 9b\. This step shows how important it is to balance both sides of your equation by performing the same operations on each side. This ensures the equation remains true and helps you move closer to isolating the variable.

Once the variable term is isolated, you often need to remove any coefficients (numbers multiplying the variable). This usually involves division.
In the simplified equation \-72 = 9b\, the variable \( b \) is being multiplied by \9\. To solve for \( b \), we need to divide both sides by \9\: \[\frac{-72}{9} = \frac{9b}{9}\]. By dividing both sides by \9\, the equation simplifies to \b = -8\.
Division is a crucial step when you need to eliminate the coefficient and solve for the variable. Just remember to apply the division to both sides to keep the equation balanced.

Simplification is essential when solving equations. It involves combining like terms and performing arithmetic operations to make the equation as simple as possible.
In our example, starting from \[-77 = 9b - 5\], we added \+5\ to both sides to simplify to \[-72 = 9b\]. Then, we divided both sides by \9\ to get \b = -8\.
Simplification ensures that each step of the process is straightforward and manageable. This way, you don't get lost in complex arithmetic. Always aim to break down equations into simpler forms to make the solution more accessible.