Question

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

Answer 1

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.

Answer 2

3 <x

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