Question

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

Answer 1

Option A, B and C are the correct options.

Explanation:

Inequality has been given as 6x ≥ 3 + 4(2x - 1)

By solving it further,

6x ≥ 3 + 8x - 4 [Option B is the correct option]

6x ≥ 8x - 1

6x - 8x ≥ 8x - 1 - 8x

-2x ≥ -1

2x ≤ 1

1 ≥ 2x [Option A is the correct option]

x ≤
`(1)/(2)`

Option C represents the inequality drawn on the number line.

Therefore, Options A, B and C are the correct options.

Answer 2

In order to check the different representations, we first simplify the inequality: 6x ≥ 3 + 4(2x - 1) 6x ≥ 3 + 8x - 4 1 ≥ 2x 1/2 ≥ x Looking at the simplification process, we see that the first and second options are correct representations. Moreover, if we plot the simplified inequality on a number line, then we see that the third representation is also correct. Therefore, the first, second and third representations of the inequality are correct.