Question

Which of the following is not a way to represent the solution of the inequality 3(2x − 1) greater than or equal to 4(2x − 3) − 3? (1 point)

A) x less than or equal to 6
B) 6 greater than or equal to x
C) A number line with a closed circle on 6 and shading to the left
D)A number line with a closed circle on 6 and shading to the right

Answer 1

3(2x - 1) > = 4(2x - 3) - 3
6x - 3 > = 8x - 12 - 3
6x - 3 > = 8x - 15
6x - 8x > = -15 + 3
-2x > = -12
x < = -12/-2
x < = 6


the incorrect one is : A number line with a closed circle on 6, shading to the right

Answer 2

Option D). is the option.

Explanation:

The given inequality is 3(2x - 1) ≥ 4(2x - 3) - 3

Now we will solve the inequality to get the answer.

3(2x -1) ≥ 4(2x - 3) - 3

6x - 3 ≥ 8x - 12 - 3 (distribution law)

6x -3 + 3 ≥ 8x - 12 - 3 + 3

6x ≥ 8x - 12

By adding 12 on both the sides

6x + 12 ≥ 8x -12 + 12

Now we will subtract 6x from both the sides

6x - 6x + 12 ≥ 8x -6x

12 ≥ 2x

2x/2 ≤ 12/2

x ≤ 6

So option D) A number line with a closed circle on 6 and shading to the right is incorrect. Rest all options are correct.