Question

1. select all the expressions that are equivalent to 8 - 12 - (6 + 4).

□ a. (6 + 4) - 8 - 12
□ b. 8 - 6 - 12 + 4
□ c. 8 - 12 - 6 - 4
□ d. 8 - (6 + 4) - 12
□ e. (8 - 12) - 6 + 4

1. which equation is equivalent to 1/3 m+1/2 n = 9?

a. 3m + 2n = 9 b. 2m + 3n = 54
c. m + 3n = 27 d. 2m + n = 18

1. explain how you know that equation a and equation b are equivalent. equation a 48 - 5x = 13 equation b 5x = 35
2. create two equivalent equations by filling in the blanks using the whole numbers 0 to 9 only once.

□x+□y = □
y = □ - □x
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Explanation:

9.

Step1: Simplify the original expression

$8 - 12-(6 + 4)=8-12 - 10=8-(12 + 10)=8 - 22=-14$

Step2: Analyze option A

$(6 + 4)-8-12=10-8 - 12=2-12=-10
eq - 14$

Step3: Analyze option B

$8-6 - 12 + 4=(8 + 4)-(6 + 12)=12-18=-6
eq - 14$

Step4: Analyze option C

$8-12-6 - 4=8-(12 + 6+4)=8 - 22=-14$

Step5: Analyze option D

$8-(6 + 4)-12=8-10 - 12=-2-12=-14$

Step6: Analyze option E

$(8 - 12)-6 + 4=-4-6 + 4=-6
eq - 14$

Step1: Clear the fractions in $\frac{1}{3}m+\frac{1}{2}n = 9$

Multiply each term of the equation by the least - common multiple of 3 and 2, which is 6.
$6\times\frac{1}{3}m+6\times\frac{1}{2}n=6\times9$

Step2: Simplify the left - hand side

$2m + 3n=54$

Step1: Start with Equation A $48-5x = 13$

We want to isolate the term with $x$.

Step2: Subtract 48 from both sides

$48-5x-48=13 - 48$
$-5x=-35$

Step3: Multiply both sides by - 1

$5x = 35$ which is Equation B.

Answer:

C. $8 - 12-6 - 4$, D. $8-(6 + 4)-12$

10.