Final answer:
The question involves solving an algebraic equation using properties such as the Distributive Property and rules for the signs of numbers during multiplication and subtraction. Substituting given values relates to evaluating expressions following the same properties and the order of operations.
Step-by-step explanation:
Properties of Numbers in Equations
When solving equations, it's important to understand the properties of numbers. In the given problem, John was asked to solve 4(2a + 3)= -3(a - 1) + 31 - 11. The student needs to simplify and solve for the variable by applying various properties such as the Distributive Property, which allows you to multiply a number by a sum or difference within parentheses, and the rules of addition and multiplication of numbers with different signs.
Regarding the mathematical rules provided:
• Rule 5: When two positive numbers multiply, the result is positive (2x3 = 6).
• Rule 6: When two negative numbers multiply, the result is positive ((-4) x (-3) = 12).
• Rule 7: When two numbers with opposite signs multiply, the result is negative ((-3) x 2 = -6).
• Rule 8: Division follows multiplication rules for signs.
Also, subtraction involves changing the sign of the value being subtracted and then following the rules of addition.
As for evaluating expressions with given values, we substitute those values into the expressions and compute the results based on these rules. For example, given x = -2, y = -4, z = 8, we would substitute these into any expression and then apply the order of operations: parentheses, exponents, multiplication and division (from left to right), and finally addition and subtraction (from left to right).