Question

Complete the following stepped-out solution to show that −7+[(8⋅m)⋅1/8]+7 is equivalent to m.

Answer 1

-7+7[(8*m)*1/8]
Commutative property of Addition

Answer 2

Enter the numbers that make the algebraic expressions equivalent.

Expression 1: 4x + 5 (x - 2) + ?
Expression 2: ?x - 11 - x + 9

Answer 3

To show that −7+[(8⋅m)⋅1/8]+7 is equivalent to m, we need to simplify the expression step by step.

Step 1: Distribute the multiplication inside the parentheses
-7 + [8 * m * 1/8] + 7

Step 2: Simplify the multiplication inside the brackets
-7 + [8m * 1/8] + 7

Step 3: Multiply 8m and 1/8
-7 + (8m * 1/8) + 7
-7 + (8m/8) + 7
-7 + (m) + 7

Step 4: Combine like terms
(-7 + 7) + m
0 + m
m

Therefore, −7+[(8⋅m)⋅1/8]+7 is equivalent to m.

Answer 4

To apply the commutative property of addition, we can rearrange the terms in the expression -7+7[(8*m)*1/8].

The commutative property of addition states that the order of addition does not affect the result.

Rearranging the terms:

-7 + 7[(8*m)*1/8]
= 7[(8*m)*1/8] + (-7)

Now we can proceed with simplifying the expression.

Answer 5

To find the numbers that make the two algebraic expressions equivalent, we need to set the expressions equal to each other and solve for the missing values.

Setting Expression 1 equal to Expression 2:

4x + 5(x - 2) + ? = ?x - 11 - x + 9

First, let's simplify the expression:

4x + 5x - 10 + ? = ?x - x - 2

Combining like terms:

9x - 10 + ? = ?x - 2

Since we don't have any numbers in the given expressions, we'll assume that the missing values are numbers.

The numbers that make the two algebraic expressions equivalent are 9 for the value of "?" in Expression 1 and -8 for the value of "?" in Expression 2.

Therefore:

Expression 1: 4x + 5(x - 2) + 9
Expression 2: -8x - 11 - x + 9