Question

Which compound inequality could this graph be the solution of?

Answer 1

B.. 4 is less than or equal to x, 2 is greater or equal to x

Answer 2

B. 2x + 3 ≥ 11 or 4x - 7 ≤ 1

Explanation:

Given compound inequality,

In option A,

2x + 3 ≥ 11 and 4x - 7 ≤ 1

⇒ 2x ≥ 8 and 4x ≤ 8

⇒ x ≥ 4 and x ≤ 2

`\implies [4,\infty)\cap (-\infty, 2]`

`=\phi`

2x + 3 ≥ 11 and 4x - 7 ≤ 1 can not be the correct inequality,

In option B,

2x + 3 ≥ 11 or 4x - 7 ≤ 1

⇒ 2x ≥ 8 or 4x ≤ 8

⇒ x ≥ 4 or x ≤ 2

`\implies [4,\infty)\cup (-\infty, 2]`

Which is shown in the given graph,

Thus, 2x + 3 ≥ 11 or 4x - 7 ≤ 1 is the correct compound inequality,

In option C,

2x + 3 > 11 or 4x - 7 < 1

⇒ 2x > 8 or 4x < 8

⇒ x > 4 or x < 2

`\implies (4,\infty)\cup (-\infty, 2)`

So, which is not shown in the graph,

2x + 3 > 11 or 4x - 7 < 1 can not be the correct compound inequality,

In option D,

2x + 3 ≥ 11 or 4x - 7 ≥ 1

⇒ 2x ≥ 8 or 4x ≥ 8

⇒ x ≥ 4 or x ≥ 2

`\implies [4,\infty)`

Which is not shown in the graph,

2x + 3 ≥ 11 or 4x - 7 ≥ 1 is not the correct compound inequality.