Which is the correct example of the distributive property?
a, 1/2(6x+12)
6x+6
b, 1/2(6x+12)
3x+6
c, 1/2(6x+12)
12x+24
d, 1/2(6x+12
3x+12

B. 1/2 (6x + 12) = 3x + 6

Step-by-step explanation:

= 1/2 (6x + 12)

= 1/2(6x) + 1/2(12)

= 6x/2 + 12/2

= 3x + 6

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true