1/2(3g - 2) = g/6 what does g equal ?

Question

and also could youh answer this too ?

tripiling thr greater of two consecutive even integers gives the same result as subtracting 10 from the lesser even integer. what are the integers?

with an explanation of how you got them both

Answer 1

1/2(3g-2)=g/6
so,3g-2=2g/6 (multiplying both sides by 2 yields)
so,3g-2=g/3
so,3g=(g/3)+2 (adding 2 both sides yields)
so,3g=(g+6)/3
so,9g=g+6 (multiplying both sides by 3 yields)
so,8g=6
so,g=6/8=3/4 (dividing both sides by 8 yields)
g=3/4

in the second one the two integers are -8 and -6
for this you should make equations .
suppose two consecutive integers are x and x+2.
trippling the greater integer will give 3(x+2) what is equal to substracting 10 from the lesses integer gives x-10. they are equal.
so,3(x+2)=x-10 solving the equation will give x=-8 so the other one will be x+2 is -6.

Answer 2

>>1/2(3g - 2) = g/6<<

1/2(3g - 2) = g/6 (now, multiply through by 6 to eliminate the fractions)
3(3g - 2) = g (now, multiply out the left side)
9g - 6 = g (now, isolate the variable on the left side)
8g = 6 (now, divide by 8)
g = 6/8, which reduces to 3/4

"Plug and chug" to test the answer:

1/2(3[3/4] - 2) ?= [3/4]/6
1/2(3[3/4] - 2) ?= 3/24
1/2([9/4] - 2) ?= 1/8
1/2([9/4] - 8/4) ?= 1/8
1/2(1/4) ?= 1/8
1/8 = 1/8


>>tripling the greater of two consecutive even integers gives the same result as subtracting 10 from the lesser even integer. what are the integers?<<

x = first integer
x + 2 = second, or greater integer (consecutive evens [or odds] differ by 2)

3(x + 2) = x - 10 (now, multiply out the left side)
3x + 6 = x - 10 (now, isolate the variable on the left side)
3x - x = -10 - 6
2x = -16 (now, divide by 2)
x = -8 (so -8 should be the first integer, and.....)

x + 2 = ?
-8 + 2 = -6 (so -6 should be the second, or greater integer)

Test the condition:

3((-8) + 2) ?= -8 - 10
3(-6) ?= -18
-18 = -18

Answer 3

1/2(3g-2)=g/6
3g-2=g/3 multiply both sides by 2
3(3g-2) = g multiply both sides by 3
9g-6 = g distibute the 3 into the parenthases
9g -6 -g = 0 subtract g from both sides
8g = 6 add 6 to both sides
g= 6/8 divide both sides by 8



for the second part
if (i-2) is an even integer, then the next greater even integer would be (i)
3i=(i-2)-10
3i=i-12
2i=-12
i=-6

i-2=?
-6-2 = -8
the two integers are -6 and -8

Answer 4

Why do expect others to do your homework for you? We won't be there come test time.