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To solve a linear equation, our main goal is to find the value of the unknown variable. In this case, the variable is represented by the letter **b**.

Isolating the variable means getting the term with **b** alone on one side of the equation. We want to make sure that **b** is by itself without any multiplied numbers or additional terms.

For the given equation \(-7b = 0\), we need to eliminate the \-7\ that is multiplied with **b**.

We can achieve this by performing an operation that will cancel out the \(-7\) on the left side of the equation. The most effective way to do this is through division because the opposite of multiplication is division.

Next, we will divide both sides of the equation by \-7\ to isolate the variable **b**.

When we isolate the variable, we then need to simplify both sides of the equation to determine the value of **b**. This involves performing basic arithmetic calculations.

After dividing both sides of the equation by \-7\, we have:

\(\frac{-7b}{-7} = \frac{0}{-7} \)

On the left side, \(-7\) and \(-7\) cancel each other out, leaving us with **b**. On the right side, \(\frac{0}{-7}\) simplifies to 0 because dividing zero by any number results in zero.

So, we now have: \[ b = 0 \]

Simplifying both sides ensures that the equation is in its simplest form, and we can clearly see the value of the variable.

Coefficients are numbers that are multiplied by variables in an equation. In our equation \(-7b = 0\), the coefficient is \(-7\).

It's important to understand that the coefficient affects how we isolate the variable. Here are some points to remember about coefficients:

• \(-7\) indicates that **b** is being multiplied by \(-7\).
• To isolate **b**, we divide by the coefficient (which in this case is \(-7\)).
• Coefficients can be positive or negative, but the process of isolating the variable remains the same.

By dividing both sides by the coefficient, we work towards making the variable stand alone, thus solving the equation.

Understanding coefficients gives us the tools needed for the crucial step of isolating the variable, leading us to the solution.