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)

A) 48m + 12 and 3(2m + 4 + 14m)

B) 48m + 12 is equivalent to 6(m + 2 + 7m) because if you distribute the 6 to everything inside the parentheses, you get 6m + 12 + 42m. This can be simplified further by adding 6m and 42m together, leaving you with 48m + 12.

C) m = 2

6(m + 2 + 7m)

6[2 + 2 + 7(2)]

6(4 + 14)

6(18)

108

3(2m + 4 + 14m)

3[2(2) + 4 + 14(2)]

3(4 + 4 + 28)

3(8 + 28)

3(36)

108

108 = 108

Step-by-step explanation:

A) You can simplify 6(m + 2 + 7m) by distributing the 6, (after simplification) resulting in 48m + 12.

Since 6/3 = 2, you can replace the 6 with 3 and multiply everything within the parentheses by 2.

B) This part was explained in the answer. If you have further questions please ask :)

C) I substituted m for 2 in both 6(m + 2 + 7m) and 3(2m + 4 + 14m). Since they both equal 108, the equations are equivalent.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

c

step-by-step explanation: