Final answer:
Each step in solving the algebraic equation involves justification using rules of arithmetic operations and properties of equality. Starting from distribution and combining like terms to isolating the variable and solving, each step adheres to the rules of arithmetic and algebra.
Step-by-step explanation:
To justify each step in solving the given algebraic equation, we need to explain the mathematical principles used at each stage as follows:
- Step A: Distribute -2.5 into the parentheses (-2 - 3x) and 2.5 into (-4x - 1). According to the multiplication rules, a negative number multiplied by a positive number gives a negative result. So, -2.5 times -2 gives +5, and -2.5 times -3x gives 7.5x.
- Step B: Combine like terms. This is when you add or subtract the coefficients of the same variable or simplify constants.
- Step C: Reduce the equation by combining like terms again on both sides to simplify the equation further.
- Step D: Transfer terms from one side of the equation to the other to isolate the variable (x) on one side. This invokes the principle of maintaining equality by performing the same operation on both sides of the equation.
- Step E: Divide both sides of the equation by the coefficient of the variable x to solve for x. By division rules, dividing by a negative number reverses the sign.
- Step F: The final step is to verify whether the solution is reasonable, ensuring that the equation balances when x is substituted with the derived value.