Question

Which of the following is not a way to represent the solution of the inequality 2(x − 2) less than or equal to 2?

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 equal to 3

Answer 1

The answer is A  A number line with a closed circle on 3-

Answer 2

The correct option is 1.

Explanation:

The given inequality is

`2(x-2)\leq 2`

Divide both the sides by 2.

`(2(x-2))/(2)\leq (2)/(2)`

`(x-2)\leq 1`

Add 2 on both the sides.

`x-2+2\leq 1+2`

`x\leq 3`

The value of x is than or equal to 3. In other words 3 greater than or equal to x.

Since the sign of inequality is ≤, therefore a number line with a closed circle on 3 and shading to the left represent the above inequality.

Only the statement "A number line with a closed circle on 3 and shading to the right" is not is not a way to represent the solution of the given inequality.

Therefore the correct option is 1.