12 − x = 7x + 32
step 1: -x = 7x + 20
step 2: -8x = 20
a.
the multiplication property of equality
b.
the division property of equality
c.
the subtraction property of equality
d.
the addition property of equality

C. the subtraction property of equality

Step-by-step explanation:

12-x = 7x + 32

Step - 1: -x = 7x + 20

In that case, we just swap 12 from the left side to right side, and then we subtract 12 from 32 which is on the right side. Therefore, we do not multiply, divide or add anything. So, the option "C" is correct.

Step 2: -8x = 20

In that case, we again subtract 12 by interchanging the side. Moreover, we change the side of 7x to deduct it from -x.

Therefore, in both the cases, we use the subtract property of equality.

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .

c) the median for town a 30" is greater than the median for town b 25"

step-by-step explanation:

town a, median = q2 = 30

town b, median - q2 = 25

so the median for town a 30" is greater than the median for town b 25"