Question

Please answer this before 5 hours have passed ^.^

An expression is shown below:

4(m + 3 + 5m)

Part A: Write two expressions that are equivalent to the given expression. (3 points)

Part B: Show that one of your expressions in Part A is equivalent to the given expression using algebraic properties. Explain which properties you used. (4 points)

Part C: Show that your other expression from Part A is equivalent to the given expression by substituting a number for m. (3 points)

Answer 1

24m + 12 - - - (1)

12(2m + 1) - - - (2)

Explanation:

Given the expression :

4(m + 3 + 5m)

Equivalent expressions include :

24m + 12 - - - (1)

12(2m + 1) - - - (2)

Using algebaraic properties :

4(m + 3 + 5m)

We can expand :

4m + 12 + 20m

4m + 20m + 12

24m + 12

Hence,

4(m + 3 + 5m) = 24m + 12

Using Substitution:

Let m = 5

4(m + 3 + 5m)

4(5 + 3 + 5(5))

4(5 +3 + 25)

4(33)

= 132

12(2m + 1)

12(2(5) + 1)

12(10 + 1)

12(11)

= 132