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Linear equations are equations of the first order. These types of equations are fundamental in algebra and show a linear relationship between variables. To solve a linear equation, our goal is simple: isolate the variable on one side of the equation. This means we manipulate the equation to find what value the variable holds. Let's look at the different steps involved:

• First, simplify both sides of the equation if needed.
• Next, get all the variable terms on one side and constants on the other.
• Finally, solve for the variable by performing the necessary arithmetic operations.

An example can reinforce these steps. Consider the linear equation from the exercise: \[ 18-(9r+7)=-16 \]
The first move is to simplify the left side. The equation then becomes: \[ 11 - 9r = -16 \]
Now, we need to isolate the term with the variable:
\[ -9r = -27 \]
Finally, solve for the variable:
\[ r = 3 \]
By systematically following these steps, solving linear equations becomes easier.

Simplifying equations is an important step in solving linear equations. It helps make the equation more manageable and easier to solve. To simplify an equation, follow these steps:

• Distribute any constants across parentheses.
• Combine like terms on each side of the equation.

In our example: \[ 18 - (9r + 7) = -16 \]
First, distribute the negative sign across the terms inside the parentheses: \[ 18 - 9r - 7 = -16 \]
Next, combine like terms. Here, we combine 18 and -7 to get: \[ 11 - 9r = -16 \]
This step reduces the complexity of the equation and sets the stage for isolating the variable. Break down complicated expressions into simpler ones by distributing and combining terms, making further manipulation easier.

Combining like terms helps to simplify algebraic expressions and equations. Like terms are terms that have the same variables raised to the same power. You can combine them by adding or subtracting their coefficients. The steps are straightforward:

• Identify like terms.
• Add or subtract their coefficients.

In our example: \[ 18 - (9r + 7) \]
We first rewrite the terms to make it clear: \[ 18 - 9r - 7 \]
Now, combine the constant terms, 18 and -7, which gives us: \[ 11 - 9r = -16 \]
It simplifies the expression and brings clarity.
When solving linear equations, combining like terms is a crucial skill. Ensuring terms are properly combined paves the way for a smooth and error-free solution process, making the rest of the calculations much easier.