The correct answers are:
A) 1 ≥ 2x ; B) 6x ≥ 3 + 8x – 4 ; and .5 shaded to the left
Step-by-step explanation:
Our inequality given is 6x ≥ 3 + 4(2x - 1). First we use the distributive property:
6x ≥ 3 + 4(2x) + 4(-1)
6x ≥ 3 + 8x - 4
This means A is correct.
Next we can subtract 8x from each side:
6x-8x ≥ 3+8x-4-8x
-2x ≥ 3-4
-2x ≥ -1
Divide both sides by -1 (remember to flip the inequality symbol):
-2x/-1 ≥ -1/-1
2x ≤ 1
This can also be written as 1 ≥ 2x, so B is correct.
To finish solving this, divide both sides by 2:
2x/2 ≤ 1/2
x ≤ 0.5
To graph this, we circle 0.5 and fill it in (since it is less than or equal to), and shade to the left (since it is less than).