Question

100 points!
An expression is shown below:

6(m + 2 + 7m)

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

$\huge\mathbb\fcolorbox{purple}{Green}{☆AnSwER♡}$

Few expression are shown below :-

6(2m+2+6m) , 6 (3m + 2+4m) , 3 (2m+4+14m)

6(m+2+7m)

Equivalent expression include:-

6(8m+2)

48m +12

6(2m+2+6m) , 6 (3m + 2+4m) , 3 (2m+4+14m)

Putting the value of m = 1 we get

6(m+2+7m) = 6(1+2+7)=60

6(2m+2+6m) = 6(2+2+6) = 60

Similarly we will put the value till 3(2m +4+14m) = 60

48m + 12 = (48×1 +12)=60

This proves that all values are equal. Hence verification is done.

Learn More:-

To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12. If we know the value of our variables, we can replace the variables with their values and then evaluate the expression.

To get the answer, solve the equation for the variable. Then plug that variable value into the expression and simplify to get the answer.

❤️

Answer 2

Few expression are shown below :-

6(2m+2+6m) , 6 (3m + 2+4m) , 3 (2m+4+14m)

6(m+2+7m)

Equivalent expression include:-

6(8m+2)

48m +12

6(2m+2+6m) , 6 (3m + 2+4m) , 3 (2m+4+14m)

Putting the value of m = 1 we get

6(m+2+7m) = 6(1+2+7)=60

6(2m+2+6m) = 6(2+2+6) = 60

Similarly we will put the value till 3(2m +4+14m) = 60

48m + 12 = (48×1 +12)=60

This proves that all values are equal. Hence verification is done.