Question

Which are correct representations of the inequality 6x ≥ 3 + 4(2x – 1)? Check all that apply.

A=1 ≥ 2x
B=6x ≥ 3 + 8x – 4
and on a graph
.5 shaded to the left
- .5 shaded to the right
.5 shaded to the right

Answer 1

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).

Answer 2

checking all that apply the correct answers would be A B and C