Question

Which of the following is not a way to represent the solution of the inequality 5(x + 2) greater than or equal to 7x + 2(x − 1)? . A number line with a closed circle on 3 and shading to the right. . A number line with a closed circle on 3 and shading to the left. . 3 greater than or equal to x . x less than or greater to 3

Answer 1

option: B is correct.

( A number line with a closed circle on 3 and shading to the left ).

Explanation:

We are asked to find which of the following is not a way to represent the solution of the inequality 5(x + 2) greater than or equal to 7x + 2(x − 1) i.e. we are given a inequality as:

`5(x+2)\geq7x+2 (x-1)`

i.e.
`5x+10\geq7x+2x-2`

i.e.
`5x+10\geq9x-2`

`10+2\geq9x-5x\\\\12\geq4x\\\\x\leq3`

Hence, the region in the number line is:

(-∞,3]

Hence, we get a number line with a closed circle at 3 and shaded region to the left of 3.

Hence Option B is correct.

( A number line with a closed circle on 3 and shading to the left ).

Answer 2

For this case we have the following inequality:

`image`

We must rewrite the inequality to find the solution.

By doing distributive property we have:

`image`

Adding similar terms we have:

`image`

Combining similar terms:

`image`

Rewriting we have:

`image`

Clearing the value of x we have:

`image`

`image`

Therefore, the solution set is:

(-∞, 3]

Answer:

The following is not a way to represent the solution of the inequality:

A number line with a closed circle on 3 and shading to the right