Which number line represents the solution set for the inequality 3(8 - 4x) < 6(x - 5 )

3 <x

Step-by-step explanation:

3(8 - 4x) < 6(x - 5 )

Divide each side by 3

3/3(8 - 4x) < 6/3(x - 5 )

8 -4x < 2(x-5)

Distribute

8 -4x < 2x-10

Add 4x to each side

8 -4x+4x < 2x+4x-10

8 < 6x-10

Add 10

8+10< 6x-10+10

18<6x

Divide by 6

18/6 < 6x/6

3 <x

Start by distributing on both sides of this inequality.

This gives you 24 - 12x < 6x - 30.

Put your x's together on the left by subtracting 6x from both sides.

This gives you 24 - 18x < -30.

Now subtract 24 from both sides to get -18x < -54.

Now divide both sides by -18 and x > 3.

Remember to switch the direction of the inequality sign

when you divide both sides by a negative number.

I have also graphed it below on the number line.

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)