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The distributive property allows us to eliminate parentheses and simplify expressions by distributing a single term across the terms inside the parentheses. The basic formula for the distributive property is: \( a(b + c) = ab + ac \).
This property is especially useful when solving equations that include parentheses. For example, when we see \(2(x - 1.3)\), we can apply the distributive property. We distribute the 2 to both \(x\) and \(-1.3\):

• First, we multiply \(2\) by \(x\), which gives us \(2x\).
• Second, we multiply \(2\) by \(-1.3\), which gives us \(-2.6\).

So the expression \(2(x - 1.3)\) becomes \(2x - 2.6\). By using the distributive property, complex terms are expanded and simplified, making it easier to solve the next steps of the equation.

Isolating the variable involves manipulating an equation so the variable (often denoted as \(x\) or another letter) stands alone on one side of the equation. This is crucial to find the solution of the variable.
To isolate, we perform operations that reverse what has been done to the variable. In the equation \(2x - 2.6 = 5.8\), we need to move the constant \(-2.6\) from the left side to the right. To do this, we add \(2.6\) to both sides:

• Left side: \(2x - 2.6 + 2.6 = 2x\)
• Right side: \(5.8 + 2.6 = 8.4\)

After adding \(2.6\) to each side, we have \(2x = 8.4\). These steps ensure that the variable part is isolated, setting up the equation to be solved.

Simplifying equations means performing all necessary arithmetic and algebraic operations to bring the equation to its most basic form. Simplifying helps us clearly see the equation's structure and solve for unknown variables.
After isolating the variable in the equation \(2x = 8.4\), our next task is to solve for \(x\). To do this, we need to divide both sides of the equation by 2:

• Left side: \(\frac{2x}{2} = x\)
• Right side: \(\frac{8.4}{2} = 4.2\)

Simplifying by dividing both sides by the same number ensures that the equation remains balanced, leading us directly to the solution \(x = 4.2\). This process of simplifying makes handling and interpreting the equation straightforward, as we've now reduced it to a form that easily reveals the value of the unknown variable.