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Making equations easier to work with is crucial when solving them. Simplification often involves expanding brackets, as each term outside the parentheses should be multiplied by every term inside. Take the equation provided: \[1.06s - 0.01(240 - s) = 22.67s\]We expand the term by multiplying each part inside the parentheses by \(0.01\), leading to: \[1.06s - 0.01 \times 240 + 0.01 \times s = 22.67s\]This can transform complex equations into simpler forms, making it easier to handle.
After expansion, we simplify further by performing operations like addition or subtraction where needed, resulting in:\[1.06s - 2.4 + 0.01s = 22.67s\]This step reduces the equation to simpler terms, making it straightforward to progress to the next steps.

To solve an equation, you need to find the value of the unknown variable by isolating it. This means keeping the variable on one side of the equals sign while moving all the other terms to the opposite side. For our equation: \[1.07s - 2.4 = 22.67s\]We start by moving all terms containing the variable to one side. In this case, move the \(22.67s\) term to the left side: \[1.07s - 22.67s = 2.4\]This process usually involves adding or subtracting terms, and performing the same operation on both sides of the equation to keep it balanced.
Finally, simplify the result. Here, we simplify to:\[-21.6s = 2.4\]The goal is to get \( s \) by itself to find its value.

Combining like terms involves simplifying an equation by adding or subtracting the coefficients of the same variables. This step is vital for ensuring clarity throughout the solving process. In our case: \[1.06s + 0.01s\]The terms correspond to the variable \(s\). Add them together to consolidate terms into one: \[1.07s\]This makes handling the equation easier by reducing the number of terms you deal with.
When working with equations, it's essential to group all similar variable terms together, as it allows for a clearer path to isolating the variable and ultimately solving the equation.