91Ó°ÊÓ

When faced with a linear equation that includes parentheses, like this one: $$18-(9r+7)=-16$$, the first step is to distribute and simplify.

Distributing means to apply any operations, such as multiplication or subtraction, to all terms inside the parentheses. In our example, we distribute the subtraction across each term inside the parentheses:
$$18 - 9r - 7 = -16$$

Once distributed, you then simplify by combining like terms. In this case, combine the constants (or the numbers without variables):
$$18 - 7 = 11$$

So, the equation simplifies to:
$$11 - 9r = -16$$
By breaking this initial step into smaller parts, it becomes easier to manage and less overwhelming. Breaking it into more digestible pieces helps in understanding the overall process of solving linear equations.

After simplifying, the next step is to isolate the variable term. This means moving everything that isn't the variable to the other side of the equation.

To isolate the variable in our equation $$11 - 9r = -16$$, we need to get rid of the 11 on the left side. You do this by subtracting 11 from both sides of the equation. This keeps the equation balanced.
$$11 - 9r - 11 = -16 - 11$$

Simplify this to get:
$$-9r = -27$$
Remember, isolating the variable is all about getting closer to having the variable alone on one side of the equation, making the next steps easier.

The final step is to solve for the variable, which now stands alone with a coefficient. The equation at this stage is:
$$-9r = -27$$

To solve for the variable, you need to isolate the variable completely. You do this by dividing both sides of the equation by the coefficient of the variable, which is -9 in this case. So, divide both sides by -9:
$$\frac{-27}{-9}$$

This simplifies to:
$$r = 3$$

Congratulations! You've successfully solved the linear equation. The solution is:
$$r = 3$$
By following these steps, you can solve any linear equation. Just remember to distribute and simplify, isolate the variable term, and solve for the variable.