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 \\(\frac{1}{3}m+\frac{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

1. create two equivalent equations by filling in the blanks using the whole numbers 0 to 9 only once.

□x+□y = □
y = □ - □x
reflection

1. circle the problem you feel most confident about.

Explanation:

9.

Step1: Simplify the original expression

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

Step2: Simplify option A

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

Step3: Simplify option B

$8-6 - 12 + 4=2-12 + 4=-10 + 4=-6$

Step4: Simplify option C

$8-12 - 6 - 4=-4-6 - 4=-10 - 4=-14$

Step5: Simplify option D

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

Step6: Simplify option E

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

Step1: Get a common - denominator for the left - hand side of the equation

$\frac{1}{3}m+\frac{1}{2}n = 9$. Multiply through by the least common multiple of 3 and 2, which is 6.
$6\times(\frac{1}{3}m+\frac{1}{2}n)=6\times9$

Step2: Distribute the 6

$6\times\frac{1}{3}m+6\times\frac{1}{2}n = 54$
$2m + 3n=54$

Step1: Start with Equation A

$48-5x = 13$.

Step2: Isolate the term with $x$

Subtract 48 from both sides: $48-5x-48=13 - 48$.
This gives $-5x=-35$.

Step3: Solve for $x$

Multiply both sides by - 1: $5x = 35$, which is Equation B.

Answer:

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

10.