Examine the expression (7 + 8) + 11. Following the order of operations, this expression simplifies to (15) + 11 = 26.
Reorder the grouping symbols to enclose the last two terms instead of the first two: 7 + (8 + 11). Do not reorder the terms; that is the commutative law of addition.
Solve for the new grouped terms and simplify the expression to check for equality: 7 + (19) = 26. Therefore, (7 + 8) + 11 and 7 + (8 + 11) are equivalent expressions and have the same numerical value.
Examine the expression (5 + 3x) + 6. Once the parentheses are removed and the like terms are combined, the sum of this expression is 11 + 3x.
Regroup the terms within the expression: 5 + (3x + 6).
Simplify the second expression to check for equality. Remove the parentheses and combine like terms: 5 + 3x + 6 = 11 + 3x. Therefore, the equivalent expressions are (5 + 3x) + 6 = 5 + (3x + 6).
Examine the expression (-9 x -4) x -2. Following the order of operations to simplify the expression, the product of the terms is (36) x -2 = -72.
Regroup the terms within the expression: -9 x (-4 x -2).
Follow the order of operations to simplify the expression and check for equality: -9 x (8) = -72.
Examine the expression (5n x 4n) x 6. Simplify the expression by removing the parentheses and combining like terms. In this case, 5n x 4n x 6 = 20n^2 x 6.
Regroup the terms to create an equivalent expression: 5n x (4n x 6).
Simplify the expression for equality: 5n x 4n x 6 = 20n^2 x 6.