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When solving linear equations, one important step is to combine like terms. Like terms are terms that have the same variable raised to the same power. In the given equation, \[ 3p - 7p = 24 \] the terms \(3p\) and \(7p\) are like terms because they both contain the variable \(p\). To simplify, you perform the arithmetic operation on their coefficients (numbers in front of the variable). Here, the coefficients are \(3\) and \(-7\), so you subtract: \[ 3p - 7p = -4p \] Once you combine the terms, the equation simplifies to \[ -4p = 24 \] Combining like terms helps to make the equation easier to solve. It reduces the number of terms and focuses on the variable and its coefficient. Break it down step by step, and don't rush through it.

The next step in solving the equation is isolating the variable. In this case, the variable is \(p\). To isolate \(p\), you need to 'undo' the operation attached to it. The current simplified equation is: \[ -4p = 24 \] Since \(p\) is being multiplied by \(-4\), you perform the inverse operation, which is division. Divide both sides of the equation by \(-4\): \[ p = \frac{24}{-4} \] Simplifying this, we get: \[ p = -6 \] The variable \(p\) is now isolated and we have our solution. Always remember to perform the same operation on both sides of the equation to maintain the balance. This keeps the equation mathematically correct and leads us to the correct solution.

After finding a solution, it is crucial to verify that it satisfies the original equation. Checking the solution ensures accuracy and confirms that there were no mistakes made during the solving process. We found \(p = -6\). To check this, substitute \(p = -6\) back into the original equation: \[ 3(-6) - 7(-6) = 24 \] First, simplify each term: \[ -18 + 42 = 24 \] Now, combine the constants: \[ 24 = 24 \] Since both sides of the equation are equal, the solution \(p = -6\) is correct. Always substitute your solution back into the original equation and simplify both sides to verify the answer. This step helps catch any errors from earlier steps and increases confidence in the solution.