Final answer:
To simplify the expression, distribute and combine like terms. Substituting x = 2 into both expressions confirms their equivalence.
Step-by-step explanation:
To simplify the expression -4(5x + 2) - 6(x - 3), we can start by distributing the -4 and -6 into the parentheses. This gives us -20x - 8 - 6x + 18. Next, we can combine like terms by adding or subtracting the coefficients of the x terms and the constant terms. This gives us -26x + 10.
To justify that the expressions are equivalent using x = 2, we substitute 2 in place of x in both original and simplified expressions. The original expression becomes -4(5(2) + 2) - 6(2 - 3), which simplifies to -4(10 + 2) - 6(2 - 3) = -4(12) - 6(-1) = -48 + 6 = -42. The simplified expression becomes -26(2) + 10 = -52 + 10 = -42. Both expressions yield the same value of -42 when x = 2, confirming their equivalence.
Learn more about Simplifying algebraic expressions and evaluating them for specific values of variables