Question

1 carlo wrote the expression shown.
0.5 (6m + 8 + 4)
which expression is equivalent to carlos expression?
a 3m + 60
b 30m + 40
c 6m + 12
d 3m + 6

2 mike wrote the expression shown.
-9 (n - 3) - 4
which expression is equivalent to carlos expression?
a -5 + n
b -9n + 29
c -7 - 30m
d -9n + 23

3 which expression is equivalent to \\(\frac{1}{2}(8 - 6x + 12)\\)?
a 7x
b -13x
c -6x + 14
d -3x + 10

4 simplify the expression: 2 (5a - 4) + 6a

Explanation:

Problem 1

Step1: Combine like terms inside parentheses

$0.5(6m + (8+4)) = 0.5(6m + 12)$

Step2: Distribute 0.5 to each term

$0.5\times6m + 0.5\times12 = 3m + 6$

Problem 2

Step1: Distribute -9 to parentheses terms

$-9(n-3)-4 = -9n + 27 - 4$

Step2: Combine constant terms

$-9n + (27-4) = -9n + 23$

Problem 3

Step1: Combine like terms inside parentheses

$\frac{1}{2}((8+12)-6x) = \frac{1}{2}(20 - 6x)$

Step2: Distribute $\frac{1}{2}$ to each term

$\frac{1}{2}\times20 - \frac{1}{2}\times6x = 10 - 3x = -3x + 10$

Problem 4

Step1: Distribute 2 to parentheses terms

$2(5a-4)+6a = 10a - 8 + 6a$

Step2: Combine like terms

$(10a+6a) - 8 = 16a - 8$

Answer:

1. D. $3m + 6$
2. D. $-9n + 23$
3. D. $-3x + 10$
4. $16a - 8$